Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight

Abstract. Given a connected open set $$\Omega \subset \mathbb{R}^{N} $$ and a function w ∈LN/p(Ω) if 1 < p < N and w ∈Lr (Ω) for some r ∈(1, ∞) if p ≧ N, with $$w^{+} \not\equiv 0,$$ we prove that the positive principal eigenvalue of the problem $$ - \hbox{div}(|\nabla _{u} |^{{p - 2}} \nabla...
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Gespeichert in:

Autor*in:	Lucia, Marcello [verfasserIn] Prashanth, S.

Format:	Artikel
Sprache:	Englisch

Erschienen:	2006

Anmerkung:	© Birkhäuser Verlag, Basel 2006

Übergeordnetes Werk:	Enthalten in: Archiv der Mathematik - Birkhäuser-Verlag, 1948, 86(2006), 1 vom: Jan., Seite 79-89
Übergeordnetes Werk:	volume:86 ; year:2006 ; number:1 ; month:01 ; pages:79-89

Links:	Volltext

DOI / URN:	10.1007/s00013-005-1512-x

Katalog-ID:	OLC2049228198

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allfields	10.1007/s00013-005-1512-x doi (DE-627)OLC2049228198 (DE-He213)s00013-005-1512-x-p DE-627 ger DE-627 rakwb eng 510 050 VZ 17,1 ssgn 31.00 bkl Lucia, Marcello verfasserin aut Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2006 Abstract. Given a connected open set $$\Omega \subset \mathbb{R}^{N} $$ and a function w ∈LN/p(Ω) if 1 < p < N and w ∈Lr (Ω) for some r ∈(1, ∞) if p ≧ N, with $$w^{+} \not\equiv 0,$$ we prove that the positive principal eigenvalue of the problem $$ - \hbox{div}(\|\nabla _{u} \|^{{p - 2}} \nabla u) = \lambda w(x)\|u\|^{{p - 2}} u,\quad u \in \mathcal{D}^{{1,p}}_{0} (\Omega ), $$ is unique and simple. This improves previous works all of which assumed w in a smaller space than LN/p (Ω) to ensure that Harnack’s inequality holds. Our proof does not rely on Harnack’s inequality, which may fail in our case. Prashanth, S. aut Enthalten in Archiv der Mathematik Birkhäuser-Verlag, 1948 86(2006), 1 vom: Jan., Seite 79-89 (DE-627)129061581 (DE-600)475-3 (DE-576)014392364 0003-889X nnns volume:86 year:2006 number:1 month:01 pages:79-89 https://doi.org/10.1007/s00013-005-1512-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4325 GBV_ILN_4700 31.00 Mathematik: Allgemeines Mathematik: Allgemeines VZ AR 86 2006 1 01 79-89
spelling	10.1007/s00013-005-1512-x doi (DE-627)OLC2049228198 (DE-He213)s00013-005-1512-x-p DE-627 ger DE-627 rakwb eng 510 050 VZ 17,1 ssgn 31.00 bkl Lucia, Marcello verfasserin aut Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2006 Abstract. Given a connected open set $$\Omega \subset \mathbb{R}^{N} $$ and a function w ∈LN/p(Ω) if 1 < p < N and w ∈Lr (Ω) for some r ∈(1, ∞) if p ≧ N, with $$w^{+} \not\equiv 0,$$ we prove that the positive principal eigenvalue of the problem $$ - \hbox{div}(\|\nabla _{u} \|^{{p - 2}} \nabla u) = \lambda w(x)\|u\|^{{p - 2}} u,\quad u \in \mathcal{D}^{{1,p}}_{0} (\Omega ), $$ is unique and simple. This improves previous works all of which assumed w in a smaller space than LN/p (Ω) to ensure that Harnack’s inequality holds. Our proof does not rely on Harnack’s inequality, which may fail in our case. Prashanth, S. aut Enthalten in Archiv der Mathematik Birkhäuser-Verlag, 1948 86(2006), 1 vom: Jan., Seite 79-89 (DE-627)129061581 (DE-600)475-3 (DE-576)014392364 0003-889X nnns volume:86 year:2006 number:1 month:01 pages:79-89 https://doi.org/10.1007/s00013-005-1512-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4325 GBV_ILN_4700 31.00 Mathematik: Allgemeines Mathematik: Allgemeines VZ AR 86 2006 1 01 79-89
allfields_unstemmed	10.1007/s00013-005-1512-x doi (DE-627)OLC2049228198 (DE-He213)s00013-005-1512-x-p DE-627 ger DE-627 rakwb eng 510 050 VZ 17,1 ssgn 31.00 bkl Lucia, Marcello verfasserin aut Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2006 Abstract. Given a connected open set $$\Omega \subset \mathbb{R}^{N} $$ and a function w ∈LN/p(Ω) if 1 < p < N and w ∈Lr (Ω) for some r ∈(1, ∞) if p ≧ N, with $$w^{+} \not\equiv 0,$$ we prove that the positive principal eigenvalue of the problem $$ - \hbox{div}(\|\nabla _{u} \|^{{p - 2}} \nabla u) = \lambda w(x)\|u\|^{{p - 2}} u,\quad u \in \mathcal{D}^{{1,p}}_{0} (\Omega ), $$ is unique and simple. This improves previous works all of which assumed w in a smaller space than LN/p (Ω) to ensure that Harnack’s inequality holds. Our proof does not rely on Harnack’s inequality, which may fail in our case. Prashanth, S. aut Enthalten in Archiv der Mathematik Birkhäuser-Verlag, 1948 86(2006), 1 vom: Jan., Seite 79-89 (DE-627)129061581 (DE-600)475-3 (DE-576)014392364 0003-889X nnns volume:86 year:2006 number:1 month:01 pages:79-89 https://doi.org/10.1007/s00013-005-1512-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4325 GBV_ILN_4700 31.00 Mathematik: Allgemeines Mathematik: Allgemeines VZ AR 86 2006 1 01 79-89
allfieldsGer	10.1007/s00013-005-1512-x doi (DE-627)OLC2049228198 (DE-He213)s00013-005-1512-x-p DE-627 ger DE-627 rakwb eng 510 050 VZ 17,1 ssgn 31.00 bkl Lucia, Marcello verfasserin aut Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2006 Abstract. Given a connected open set $$\Omega \subset \mathbb{R}^{N} $$ and a function w ∈LN/p(Ω) if 1 < p < N and w ∈Lr (Ω) for some r ∈(1, ∞) if p ≧ N, with $$w^{+} \not\equiv 0,$$ we prove that the positive principal eigenvalue of the problem $$ - \hbox{div}(\|\nabla _{u} \|^{{p - 2}} \nabla u) = \lambda w(x)\|u\|^{{p - 2}} u,\quad u \in \mathcal{D}^{{1,p}}_{0} (\Omega ), $$ is unique and simple. This improves previous works all of which assumed w in a smaller space than LN/p (Ω) to ensure that Harnack’s inequality holds. Our proof does not rely on Harnack’s inequality, which may fail in our case. Prashanth, S. aut Enthalten in Archiv der Mathematik Birkhäuser-Verlag, 1948 86(2006), 1 vom: Jan., Seite 79-89 (DE-627)129061581 (DE-600)475-3 (DE-576)014392364 0003-889X nnns volume:86 year:2006 number:1 month:01 pages:79-89 https://doi.org/10.1007/s00013-005-1512-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4325 GBV_ILN_4700 31.00 Mathematik: Allgemeines Mathematik: Allgemeines VZ AR 86 2006 1 01 79-89
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author	Lucia, Marcello
spellingShingle	Lucia, Marcello ddc 510 ssgn 17,1 bkl 31.00 Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight
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topic_title	510 050 VZ 17,1 ssgn 31.00 bkl Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight
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title	Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight
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title_full	Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight
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author_browse	Lucia, Marcello Prashanth, S.
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title_sort	simplicity of principal eigenvalue for p-laplace operator with singular indefinite weight
title_auth	Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight
abstract	Abstract. Given a connected open set $$\Omega \subset \mathbb{R}^{N} $$ and a function w ∈LN/p(Ω) if 1 < p < N and w ∈Lr (Ω) for some r ∈(1, ∞) if p ≧ N, with $$w^{+} \not\equiv 0,$$ we prove that the positive principal eigenvalue of the problem $$ - \hbox{div}(\|\nabla _{u} \|^{{p - 2}} \nabla u) = \lambda w(x)\|u\|^{{p - 2}} u,\quad u \in \mathcal{D}^{{1,p}}_{0} (\Omega ), $$ is unique and simple. This improves previous works all of which assumed w in a smaller space than LN/p (Ω) to ensure that Harnack’s inequality holds. Our proof does not rely on Harnack’s inequality, which may fail in our case. © Birkhäuser Verlag, Basel 2006
abstractGer	Abstract. Given a connected open set $$\Omega \subset \mathbb{R}^{N} $$ and a function w ∈LN/p(Ω) if 1 < p < N and w ∈Lr (Ω) for some r ∈(1, ∞) if p ≧ N, with $$w^{+} \not\equiv 0,$$ we prove that the positive principal eigenvalue of the problem $$ - \hbox{div}(\|\nabla _{u} \|^{{p - 2}} \nabla u) = \lambda w(x)\|u\|^{{p - 2}} u,\quad u \in \mathcal{D}^{{1,p}}_{0} (\Omega ), $$ is unique and simple. This improves previous works all of which assumed w in a smaller space than LN/p (Ω) to ensure that Harnack’s inequality holds. Our proof does not rely on Harnack’s inequality, which may fail in our case. © Birkhäuser Verlag, Basel 2006
abstract_unstemmed	Abstract. Given a connected open set $$\Omega \subset \mathbb{R}^{N} $$ and a function w ∈LN/p(Ω) if 1 < p < N and w ∈Lr (Ω) for some r ∈(1, ∞) if p ≧ N, with $$w^{+} \not\equiv 0,$$ we prove that the positive principal eigenvalue of the problem $$ - \hbox{div}(\|\nabla _{u} \|^{{p - 2}} \nabla u) = \lambda w(x)\|u\|^{{p - 2}} u,\quad u \in \mathcal{D}^{{1,p}}_{0} (\Omega ), $$ is unique and simple. This improves previous works all of which assumed w in a smaller space than LN/p (Ω) to ensure that Harnack’s inequality holds. Our proof does not rely on Harnack’s inequality, which may fail in our case. © Birkhäuser Verlag, Basel 2006
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title_short	Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight
url	https://doi.org/10.1007/s00013-005-1512-x
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up_date	2024-07-03T21:58:59.798Z
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