TITLE

A class of integral equations and approximation of p-Laplace equations

AUTHOR(S)
Ishii, Hitoshi; Nakamura, Gou
PUB. DATE
March 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Mar2010, Vol. 37 Issue 3/4, p485
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let $${\Omega\subset\mathbb{R}^n}$$ be a bounded domain, and let 1 < p < ∞ and σ < p. We study the nonlinear singular integral equationwith the boundary condition u = g0 on ∂Ω, where $${f_0\in C(\overline\Omega)}$$ and $${g_0\in C(\partial\Omega)}$$ are given functions and M is the singular integral operator given bywith some choice of $${\rho\in C(\overline\Omega)}$$ having the property, 0 < ρ( x) ≤ dist ( x, ∂Ω). We establish the solvability (well-posedness) of this Dirichlet problem and the convergence uniform on $${\overline\Omega}$$, as σ → p, of the solution u σ of the Dirichlet problem to the solution u of the Dirichlet problem for the p-Laplace equation νΔ p u = f0 in Ω with the Dirichlet condition u = g0 on ∂Ω, where the factor ν is a positive constant (see (7.2)).
ACCESSION #
47955919

 

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