$H^{1,p}$-eigenvalues and $L^\infty$-estimates in quasicylindrical domains

Antonio Vitolo

doi:10.3934/cpaa.2011.10.1315

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2011, Volume 10, Issue 5: 1315-1329. Doi: 10.3934/cpaa.2011.10.1315

This issue Previous Article Preface Next Article Existence of chaos in weakly quasilinear systems

$H^{1,p}$-eigenvalues and $L^\infty$-estimates in quasicylindrical domains

Antonio Vitolo^1,

1.
Dipartimento di Matematica e Informatica, Università di Salerno, P. Grahamstown, Fisciano, SA I-84084

Received: February 28, 2009

Revised: October 31, 2009

Published: August 2011

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Abstract

In this paper we consider estimates of the Raleigh quotient and in general of the $H^{1,p}$-eigenvalue in quasicylindrical domains. Then we apply the results to obtain, by variational methods, existence and uniqueness of weak solutions of the Dirichlet problem for second-order elliptic equations in divergent form. For such solutions global boundedness estimates have been also established.

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Mathematics Subject Classification: Primary: 35P15, 35J25; Secondary: 35B45.

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