Non-coercive Linear Elliptic Problems

Measure Data and Numerical Schemes for Elliptic Problems

In order to show existence of solutions for linear elliptic problems with measure data, a first classical method, due to Stampacchia, is to use a duality argument (and a regularity result for elliptic problems). Another classical method is to pass to the limit on approximate solutions obtained with regular data (converging towards the measure data). A third method is presented. It consists to p...

A convergent adaptive method for elliptic eigenvalue problems and numerical experiments

We prove the convergence of an adaptive linear finite element method for computing eigenvalues and eigenfunctions of second order symmetric elliptic partial differential operators. The weak form is assumed to yield a bilinear form which is bounded and coercive in H. Each step of the adaptive procedure refines elements in which a standard a posteriori error estimator is large and also refines el...

VŠB – Technical University of Ostrava

The thesis focuses on the solution of both coercive and semi–coercive contact problems by using the Boundary Element Tearing and Interconnecting (BETI) method, which represents a boundary element counterpart of the Finite Element Tearing and Interconnecting (FETI) method. The BETI approach, which uses “tearing” the domain into non–overlapping subdomains and subsequent “gluing” along the artific...

Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)