Geodesic
Boundary behavior and estimates for solutions of equations containing the $p$-Laplacian
Electronic Journal of Differential Equations, Tome 1999 (1999).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {1999},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a63/}
}
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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/