Fleckinger, JacquelineHarrell, Evansde Thelin, Francois2019-11-212019-11-211999-09-28Fleckinger, 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. 1-20.1072-6691https://hdl.handle.net/10877/8855We 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.Text19 pages1 file (.pdf)enAttribution 4.0 Internationalp-LaplacianHardy inequalityprincipal eigenvalueboundary estimateboundary perturbationArticle