Embeddings, Hardy operators and nonlinear problems

Abstract We survey some of the recent developments involving embeddings between function spaces. Emphasis is placed on improvements of classical Sobolev inequalities, the reduction of embedding questions to problems involving Hardy operators, and quantitative estimates of compactness of embeddings t...
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Gespeichert in:

Autor*in:	Edmunds, D. E. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2009

Anmerkung:	© Revista Matemática Complutense 2009

Übergeordnetes Werk:	Enthalten in: Revista matemática complutense - Madrid : Univ., 1988, 23(2009), 2 vom: 26. Nov., Seite 267-319
Übergeordnetes Werk:	volume:23 ; year:2009 ; number:2 ; day:26 ; month:11 ; pages:267-319

Links:	Volltext

DOI / URN:	10.1007/s13163-009-0016-9

Katalog-ID:	SPR030711819

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allfields	10.1007/s13163-009-0016-9 doi (DE-627)SPR030711819 (SPR)s13163-009-0016-9-e DE-627 ger DE-627 rakwb eng Edmunds, D. E. verfasserin aut Embeddings, Hardy operators and nonlinear problems 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Revista Matemática Complutense 2009 Abstract We survey some of the recent developments involving embeddings between function spaces. Emphasis is placed on improvements of classical Sobolev inequalities, the reduction of embedding questions to problems involving Hardy operators, and quantitative estimates of compactness of embeddings that have applications to the spectral theory of operators. We also consider a nonlinear eigenvalue problem which leads to a series representation of compact linear operators acting between Banach spaces, under mild restrictions on the spaces, thus establishing a complete analogue of E. Schmidt’s classical Hilbert space theorem for compact operators. Information about relevant embedding maps enables the Dirichlet problem for the p-Laplacian to be studied, and a brief discussion is given of the generalizations of the trigonometric functions that appear naturally in this connection. Enthalten in Revista matemática complutense Madrid : Univ., 1988 23(2009), 2 vom: 26. Nov., Seite 267-319 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:23 year:2009 number:2 day:26 month:11 pages:267-319 https://dx.doi.org/10.1007/s13163-009-0016-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 23 2009 2 26 11 267-319
spelling	10.1007/s13163-009-0016-9 doi (DE-627)SPR030711819 (SPR)s13163-009-0016-9-e DE-627 ger DE-627 rakwb eng Edmunds, D. E. verfasserin aut Embeddings, Hardy operators and nonlinear problems 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Revista Matemática Complutense 2009 Abstract We survey some of the recent developments involving embeddings between function spaces. Emphasis is placed on improvements of classical Sobolev inequalities, the reduction of embedding questions to problems involving Hardy operators, and quantitative estimates of compactness of embeddings that have applications to the spectral theory of operators. We also consider a nonlinear eigenvalue problem which leads to a series representation of compact linear operators acting between Banach spaces, under mild restrictions on the spaces, thus establishing a complete analogue of E. Schmidt’s classical Hilbert space theorem for compact operators. Information about relevant embedding maps enables the Dirichlet problem for the p-Laplacian to be studied, and a brief discussion is given of the generalizations of the trigonometric functions that appear naturally in this connection. Enthalten in Revista matemática complutense Madrid : Univ., 1988 23(2009), 2 vom: 26. Nov., Seite 267-319 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:23 year:2009 number:2 day:26 month:11 pages:267-319 https://dx.doi.org/10.1007/s13163-009-0016-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 23 2009 2 26 11 267-319
allfields_unstemmed	10.1007/s13163-009-0016-9 doi (DE-627)SPR030711819 (SPR)s13163-009-0016-9-e DE-627 ger DE-627 rakwb eng Edmunds, D. E. verfasserin aut Embeddings, Hardy operators and nonlinear problems 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Revista Matemática Complutense 2009 Abstract We survey some of the recent developments involving embeddings between function spaces. Emphasis is placed on improvements of classical Sobolev inequalities, the reduction of embedding questions to problems involving Hardy operators, and quantitative estimates of compactness of embeddings that have applications to the spectral theory of operators. We also consider a nonlinear eigenvalue problem which leads to a series representation of compact linear operators acting between Banach spaces, under mild restrictions on the spaces, thus establishing a complete analogue of E. Schmidt’s classical Hilbert space theorem for compact operators. Information about relevant embedding maps enables the Dirichlet problem for the p-Laplacian to be studied, and a brief discussion is given of the generalizations of the trigonometric functions that appear naturally in this connection. Enthalten in Revista matemática complutense Madrid : Univ., 1988 23(2009), 2 vom: 26. Nov., Seite 267-319 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:23 year:2009 number:2 day:26 month:11 pages:267-319 https://dx.doi.org/10.1007/s13163-009-0016-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 23 2009 2 26 11 267-319
allfieldsGer	10.1007/s13163-009-0016-9 doi (DE-627)SPR030711819 (SPR)s13163-009-0016-9-e DE-627 ger DE-627 rakwb eng Edmunds, D. E. verfasserin aut Embeddings, Hardy operators and nonlinear problems 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Revista Matemática Complutense 2009 Abstract We survey some of the recent developments involving embeddings between function spaces. Emphasis is placed on improvements of classical Sobolev inequalities, the reduction of embedding questions to problems involving Hardy operators, and quantitative estimates of compactness of embeddings that have applications to the spectral theory of operators. We also consider a nonlinear eigenvalue problem which leads to a series representation of compact linear operators acting between Banach spaces, under mild restrictions on the spaces, thus establishing a complete analogue of E. Schmidt’s classical Hilbert space theorem for compact operators. Information about relevant embedding maps enables the Dirichlet problem for the p-Laplacian to be studied, and a brief discussion is given of the generalizations of the trigonometric functions that appear naturally in this connection. Enthalten in Revista matemática complutense Madrid : Univ., 1988 23(2009), 2 vom: 26. Nov., Seite 267-319 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:23 year:2009 number:2 day:26 month:11 pages:267-319 https://dx.doi.org/10.1007/s13163-009-0016-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 23 2009 2 26 11 267-319
allfieldsSound	10.1007/s13163-009-0016-9 doi (DE-627)SPR030711819 (SPR)s13163-009-0016-9-e DE-627 ger DE-627 rakwb eng Edmunds, D. E. verfasserin aut Embeddings, Hardy operators and nonlinear problems 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Revista Matemática Complutense 2009 Abstract We survey some of the recent developments involving embeddings between function spaces. Emphasis is placed on improvements of classical Sobolev inequalities, the reduction of embedding questions to problems involving Hardy operators, and quantitative estimates of compactness of embeddings that have applications to the spectral theory of operators. We also consider a nonlinear eigenvalue problem which leads to a series representation of compact linear operators acting between Banach spaces, under mild restrictions on the spaces, thus establishing a complete analogue of E. Schmidt’s classical Hilbert space theorem for compact operators. Information about relevant embedding maps enables the Dirichlet problem for the p-Laplacian to be studied, and a brief discussion is given of the generalizations of the trigonometric functions that appear naturally in this connection. Enthalten in Revista matemática complutense Madrid : Univ., 1988 23(2009), 2 vom: 26. Nov., Seite 267-319 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:23 year:2009 number:2 day:26 month:11 pages:267-319 https://dx.doi.org/10.1007/s13163-009-0016-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 23 2009 2 26 11 267-319
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spellingShingle	Edmunds, D. E. Embeddings, Hardy operators and nonlinear problems
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abstract	Abstract We survey some of the recent developments involving embeddings between function spaces. Emphasis is placed on improvements of classical Sobolev inequalities, the reduction of embedding questions to problems involving Hardy operators, and quantitative estimates of compactness of embeddings that have applications to the spectral theory of operators. We also consider a nonlinear eigenvalue problem which leads to a series representation of compact linear operators acting between Banach spaces, under mild restrictions on the spaces, thus establishing a complete analogue of E. Schmidt’s classical Hilbert space theorem for compact operators. Information about relevant embedding maps enables the Dirichlet problem for the p-Laplacian to be studied, and a brief discussion is given of the generalizations of the trigonometric functions that appear naturally in this connection. © Revista Matemática Complutense 2009
abstractGer	Abstract We survey some of the recent developments involving embeddings between function spaces. Emphasis is placed on improvements of classical Sobolev inequalities, the reduction of embedding questions to problems involving Hardy operators, and quantitative estimates of compactness of embeddings that have applications to the spectral theory of operators. We also consider a nonlinear eigenvalue problem which leads to a series representation of compact linear operators acting between Banach spaces, under mild restrictions on the spaces, thus establishing a complete analogue of E. Schmidt’s classical Hilbert space theorem for compact operators. Information about relevant embedding maps enables the Dirichlet problem for the p-Laplacian to be studied, and a brief discussion is given of the generalizations of the trigonometric functions that appear naturally in this connection. © Revista Matemática Complutense 2009
abstract_unstemmed	Abstract We survey some of the recent developments involving embeddings between function spaces. Emphasis is placed on improvements of classical Sobolev inequalities, the reduction of embedding questions to problems involving Hardy operators, and quantitative estimates of compactness of embeddings that have applications to the spectral theory of operators. We also consider a nonlinear eigenvalue problem which leads to a series representation of compact linear operators acting between Banach spaces, under mild restrictions on the spaces, thus establishing a complete analogue of E. Schmidt’s classical Hilbert space theorem for compact operators. Information about relevant embedding maps enables the Dirichlet problem for the p-Laplacian to be studied, and a brief discussion is given of the generalizations of the trigonometric functions that appear naturally in this connection. © Revista Matemática Complutense 2009
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