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arXiv · 1105.2545

Schwarz Symmetrization and Comparison Results for Nonlinear Elliptic Equations and Eigenvalue Problems

Leonardo Prange Bonorino·José Fábio Bezerra Montenegro
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Abstract

We compare the distribution function and the maximum of solutions of nonlinear elliptic equations defined in general domains with solutions of similar problems defined in a ball using Schwarz symmetrization. As an application, we prove the existence and bound of solutions for some nonlinear equation. Moreover, for some nonlinear problems, we show that if the first $p$-eigenvalue of a domain is big, the supremum of a solution related to this domain is close to zero. For that we obtain $L^{\infty}$ estimates for solutions of nonlinear and eigenvalue problems in terms of other $L^p$ norms.

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Leonardo Prange Bonorino, José Fábio Bezerra Montenegro. 2011-05-12. Schwarz Symmetrization and Comparison Results for Nonlinear Elliptic Equations and Eigenvalue Problems. https://doi.org/10.1007/s10231-012-0255-0

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