Comparison and Existence Results for Classes of Nonlinear Elliptic Equations with General Growth in the Gradient

Comparison and Existence Results for Classes of Nonlinear Elliptic Equations with General Growth in the Gradient

In this paper we study the Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = H(x, u, Du), where the principal term is a Leray-Lions operator defined on W (Ω), and H(x, u, Du) grows with respect to Du at most like |Du| , p-1 ≤ q ≤ p. Comparison results are obtained betw...

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Veröffentlicht in:Advanced nonlinear studies 2007-02, Vol.7 (1), p.31-46
Hauptverfasser: Ferone, Vincenzo, Messano, Basilio
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nonlinear elliptic PDE’s
rearrangement
symmetrization
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description In this paper we study the Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = H(x, u, Du), where the principal term is a Leray-Lions operator defined on W (Ω), and H(x, u, Du) grows with respect to Du at most like |Du| , p-1 ≤ q ≤ p. Comparison results are obtained between the rearrangement of a solution u of Dirichlet problem quoted above and the rearrangement of the solution of a problem whose data are radially symmetric.
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source Alma/SFX Local Collection; Walter De Gruyter: Open Access Journals
subjects nonlinear elliptic PDE’s
rearrangement
symmetrization
title Comparison and Existence Results for Classes of Nonlinear Elliptic Equations with General Growth in the Gradient
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