AN EXISTENCE AND UNIQUENESS OF THE SOLUTION OF SEMILINEAR MONOTONE ELLIPTIC EQUATION WITH THE DATA IN STUMMEL CLASSES

Abstract

Let be a bounded open subset of , , be a function in Stummel classes , where , and be a semilinear monotone elliptic equation, where is symmetric matrix, elliptic, bounded, and is non decreasing and Lipschitz. By proving a weighted estimation for a function in Stummel class with its weight in , which allows us to use Stampacchia’s lemma, we obtained the existence and uniqueness of the solution of this equation.

Keywords

• semilinear elliptic equations
• stummel classes