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TWO-SIDED ESTIMATES FOR POSITIVE SOLUTIONS OF SUPERLINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS

Part of: Elliptic equations and systems Partial differential equations

Published online by Cambridge University Press:  30 August 2018

KENTARO HIRATA
KENTARO HIRATA*
Affiliation:
Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan email hiratake@hiroshima-u.ac.jp
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Abstract

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We give two-sided estimates for positive solutions of the superlinear elliptic problem $-\unicode[STIX]{x1D6E5}u=a(x)|u|^{p-1}u$ with zero Dirichlet boundary condition in a bounded Lipschitz domain. Our result improves the well-known a priori$L^{\infty }$-estimate and provides information about the boundary decay rate of solutions.

Keywords

a priori estimatesemilinear elliptic equation

MSC classification

Primary: 35B45: A priori estimates
Secondary: 35J91: Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 465 - 473
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This work was supported in part by JSPS KAKENHI Grant Number JP18K03333.

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