Monotonicity and Enclosure Methods for the $p$-Laplace Equation

ENCLOSURE METHOD FOR THE p-LAPLACE EQUATION

We study the enclosure method for the p-Calderón problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderón that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, wh...

Enclosure for the Biharmonic Equation

In this paper we give an enclosure for the solution of the biharmonic problem and also for its gradient and Laplacian in the L2-norm, respectively.

A space mapping approach for the p-Laplace equation

The enclosure method for the heat equation

This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary value problems whose governing equation is the heat equation is considered. An explicit method to extract an approximation of the value of the support function a...

VISCOSITY SUPERSOLUTIONS OF THE EVOLUTIONARY p-LAPLACE EQUATION

has this character. Even obvious results for this equation may require advanced estimates in the proofs. We refer to the books [DB] and [WZYL] about this equation, which is called the “evolutionary p-Laplacian equation,” the “p-parabolic equation” or even the “non-Newtonian equation of filtration.”. Our objective is to study the regularity of the viscosity supersolutions and their spatial gradi...