Strong coefficient stability for quasilinear elliptic equations with application to inverse coefficient problems

Abstract

In this paper an existence, uniqueness and coefficient convergence of the solution of nonlinear boundary value problems related to quasilinear elliptic operator is studied by assuming minimal conditions on the coefficient . By using the monotonicity method it is shown that the sequence of solutions of linearised problem converges to the solution of the nonlinear problem in HI-norm. The coefficient convergence theorem for the linearised problem is proved. Then the same result HI-norm is obtained for considered nonlinear problem.

Keywords:

• Quasilinear elliptic operator
• variational method
• coefficient stability
• inverse coefficient problem