A priori regularity for weak solutions of some nonlinear elliptic equations
Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers as...
Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers...
We consider a mathematical model of a quasistatic contact between an elastic body and an obstacle. The contact is modelled with unilateral constraint and normal compliance, associated to a version of Coulomb's law of dry friction where the coefficient of friction depends on the slip displacement. We present a weak formulation of the problem and establish an existence result. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments.
In this article we produce a refined version of the classical Pohozaev identity in the radial setting. The refined identity is then compared to the original, and possible applications are discussed.
In this paper we prove a regularity result for local minimizers of functionals of the Calculus of Variations of the typewhere Ω is a bounded open set in , u∈(Ω; ), p> 1, n≥ 2 and N≥ 1. We use the technique of difference quotient without the usual assumption on the growth of the second derivatives of the function f. We apply this result to give a bound on the Hausdorff dimension of the singular set of minimizers.
We examine the p-harmonic equation div |grad u|(p-2). grad u = mu, where mu is a bounded Radon measure. We determine a range of p's for which solutions to the equation verify an a priori estimate. For such p's we also prove a higher integrability result.