Boundary Behavior and Estimates for Solutions of Equations Containing the p-Laplacian
Date
1999-09-28
Authors
Fleckinger, Jacqueline
Harrell, Evans
de Thelin, Francois
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We use ``Hardy-type'' inequalities to derive Lq estimates for solutions of equations containing the p-Laplacian with p > 1. We begin by deriving some inequalities using elementary ideas from an early article [B3] which has been largely overlooked. Then we derive Lq estimates of the boundary behavior of test functions of finite energy, and consequently of principal (positive) eigenfunctions of functionals containing the p-Laplacian. The estimates contain exponents known to be sharp when p = 2. These lead to estimates of the effect of boundary perturbation on the fundamental eigenvalue. Finally, we present global Lq estimates of solutions of the Cauchy problem for some initial-value problems containing the p-Laplacian.
Description
Keywords
p-Laplacian, Hardy inequality, principal eigenvalue, boundary estimate, boundary perturbation
Citation
Fleckinger, J., Harrell, E. M., Thelin, F. D. (1999). Boundary behavior and estimates for solutions of equations containing the p-Laplacian. <i>Electronic Journal of Differential Equations, 1999</i>(38), pp. 1-20.
Rights
Attribution 4.0 International