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

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

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