Convergence Rates in L2 for Elliptic Homogenization Problems
Abstract We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems $${\{\mathcal{L}_\varepsilon\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet,...
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| Autor*in: |
Kenig, Carlos E. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2011 |
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| Übergeordnetes Werk: |
Enthalten in: Archive for rational mechanics and analysis - Springer-Verlag, 1957, 203(2011), 3 vom: 24. Sept., Seite 1009-1036 |
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| Übergeordnetes Werk: |
volume:203 ; year:2011 ; number:3 ; day:24 ; month:09 ; pages:1009-1036 |
| Links: |
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| DOI / URN: |
10.1007/s00205-011-0469-0 |
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| 520 | |a Abstract We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems $${\{\mathcal{L}_\varepsilon\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of $${\{\mathcal{L}_\varepsilon\}}$$ . Most of our results, which rely on the recently established uniform estimates for the L2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867–917, 2011; Commun Pure Appl Math 64:1–44, 2011) are new even for smooth domains. | ||
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| 700 | 1 | |a Shen, Zhongwei |4 aut | |
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10.1007/s00205-011-0469-0 doi (DE-627)OLC205642049X (DE-He213)s00205-011-0469-0-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kenig, Carlos E. verfasserin aut Convergence Rates in L2 for Elliptic Homogenization Problems 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2011 Abstract We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems $${\{\mathcal{L}_\varepsilon\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of $${\{\mathcal{L}_\varepsilon\}}$$ . Most of our results, which rely on the recently established uniform estimates for the L2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867–917, 2011; Commun Pure Appl Math 64:1–44, 2011) are new even for smooth domains. Weak Solution Convergence Rate Dirichlet Problem Neumann Boundary Condition Neumann Problem Lin, Fanghua aut Shen, Zhongwei aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 203(2011), 3 vom: 24. Sept., Seite 1009-1036 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:203 year:2011 number:3 day:24 month:09 pages:1009-1036 https://doi.org/10.1007/s00205-011-0469-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_65 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4323 GBV_ILN_4700 AR 203 2011 3 24 09 1009-1036 |
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10.1007/s00205-011-0469-0 doi (DE-627)OLC205642049X (DE-He213)s00205-011-0469-0-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kenig, Carlos E. verfasserin aut Convergence Rates in L2 for Elliptic Homogenization Problems 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2011 Abstract We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems $${\{\mathcal{L}_\varepsilon\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of $${\{\mathcal{L}_\varepsilon\}}$$ . Most of our results, which rely on the recently established uniform estimates for the L2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867–917, 2011; Commun Pure Appl Math 64:1–44, 2011) are new even for smooth domains. Weak Solution Convergence Rate Dirichlet Problem Neumann Boundary Condition Neumann Problem Lin, Fanghua aut Shen, Zhongwei aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 203(2011), 3 vom: 24. Sept., Seite 1009-1036 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:203 year:2011 number:3 day:24 month:09 pages:1009-1036 https://doi.org/10.1007/s00205-011-0469-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_65 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4323 GBV_ILN_4700 AR 203 2011 3 24 09 1009-1036 |
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10.1007/s00205-011-0469-0 doi (DE-627)OLC205642049X (DE-He213)s00205-011-0469-0-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kenig, Carlos E. verfasserin aut Convergence Rates in L2 for Elliptic Homogenization Problems 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2011 Abstract We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems $${\{\mathcal{L}_\varepsilon\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of $${\{\mathcal{L}_\varepsilon\}}$$ . Most of our results, which rely on the recently established uniform estimates for the L2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867–917, 2011; Commun Pure Appl Math 64:1–44, 2011) are new even for smooth domains. Weak Solution Convergence Rate Dirichlet Problem Neumann Boundary Condition Neumann Problem Lin, Fanghua aut Shen, Zhongwei aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 203(2011), 3 vom: 24. Sept., Seite 1009-1036 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:203 year:2011 number:3 day:24 month:09 pages:1009-1036 https://doi.org/10.1007/s00205-011-0469-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_65 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4323 GBV_ILN_4700 AR 203 2011 3 24 09 1009-1036 |
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530 510 |
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convergence rates in l2 for elliptic homogenization problems |
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Convergence Rates in L2 for Elliptic Homogenization Problems |
| abstract |
Abstract We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems $${\{\mathcal{L}_\varepsilon\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of $${\{\mathcal{L}_\varepsilon\}}$$ . Most of our results, which rely on the recently established uniform estimates for the L2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867–917, 2011; Commun Pure Appl Math 64:1–44, 2011) are new even for smooth domains. © Springer-Verlag 2011 |
| abstractGer |
Abstract We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems $${\{\mathcal{L}_\varepsilon\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of $${\{\mathcal{L}_\varepsilon\}}$$ . Most of our results, which rely on the recently established uniform estimates for the L2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867–917, 2011; Commun Pure Appl Math 64:1–44, 2011) are new even for smooth domains. © Springer-Verlag 2011 |
| abstract_unstemmed |
Abstract We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems $${\{\mathcal{L}_\varepsilon\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of $${\{\mathcal{L}_\varepsilon\}}$$ . Most of our results, which rely on the recently established uniform estimates for the L2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867–917, 2011; Commun Pure Appl Math 64:1–44, 2011) are new even for smooth domains. © Springer-Verlag 2011 |
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Convergence Rates in L2 for Elliptic Homogenization Problems |
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