Geodesic
Boundary behavior and estimates for solutions of equations containing the \(p\)-Laplacian
Electronic journal of differential equations, Tome 1999 (1999)
We use "Hardy-type" inequalities to derive $L^{q}$ 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 $L^{q}$ 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 $L^{q}$ estimates of solutions of the Cauchy problem for some initial-value problems containing the p-Laplacian.
Classification : 35J60, 35J70
Keywords: p-Laplacian, Hardy inequlity, principal eigenvalue, boundary estimate, boundary perturbation 
@article{EJDE_1999__1999__a63,
     author = {Fleckinger,  Jacqueline and Harrell,  Evans M.II and de Th\'elin,  Fran\c{c}ois},
     title = {Boundary behavior and estimates for solutions of equations containing the {\(p\)-Laplacian}},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0928.35046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a63/}
}
TY  - JOUR
AU  - Fleckinger,  Jacqueline
AU  - Harrell,  Evans M.II
AU  - de Thélin,  François
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JO  - Electronic journal of differential equations
PY  - 1999
VL  - 1999
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LA  - en
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%A Harrell,  Evans M.II
%A de Thélin,  François
%T Boundary behavior and estimates for solutions of equations containing the \(p\)-Laplacian
%J Electronic journal of differential equations
%D 1999
%V 1999
%U http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a63/
%G en
%F EJDE_1999__1999__a63
Fleckinger,  Jacqueline; Harrell,  Evans M.II; de Thélin,  François. Boundary behavior and estimates for solutions of equations containing the \(p\)-Laplacian. Electronic journal of differential equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a63/