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

Antonio Vitolo | Zendy

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

Author(s) -

Antonio Vitolo

Publication year - 2011

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2011.10.1315

Subject(s) - uniqueness , mathematics , eigenvalues and eigenvectors , quotient , dirichlet eigenvalue , pure mathematics , dirichlet problem , dirichlet distribution , mathematical analysis , order (exchange) , boundary value problem , dirichlet's principle , physics , finance , quantum mechanics , economics

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, the existence and uniqueness of weak solutions of the Dirichlet problem for second-order elliptic equations in\uddivergent form. For such solutions global boundedness estimates have been also established

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