Solvability of nonlinear Dirichlet problem for a class of degenerate elliptic equations

Albo Carlos Cavalheiro

doi:10.1155/s1085337504310043

Abstract

We prove an existence result for solution to a class of nonlinear degenerate elliptic equation associated with a class of partial differential operators of the form , with Dj = ∂/∂xj, where aij : Ω → ℝ are functionssatisfying suitable hypotheses.

Highlights

We prove the existence of solution in D(A) ⊆ H0(Ω) for the following nonlinear Dirichlet problem: n
Where L is an elliptic operator in divergence form n
For all ξ ∈ Rn and almost every x ∈ Ω ⊂ Rn a bounded open set with piecewise smooth boundary (i.e., ∂Ω ∈ C0,1), and ω and v two weight functions

Summary

Introduction

We prove the existence of solution in D(A) ⊆ H0(Ω) for the following nonlinear Dirichlet problem: n Let the dual pairs {X, X+} and {Y , Y +} be given, where X, X+, Y , and Y + are Banach spaces with corresponding bilinear forms ·, · X and ·, · Y and the continuous embeddings Y ⊆ X and X+ ⊆ Y +. We will apply this theorem to a sufficiently large ball K in the Banach spaces X = H0(Ω), X+ = (H0(Ω))∗, and Y + = Y ∗.

Results

Conclusion