We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg group H. The model case is the nondegenerate p-Laplacean operator

In this paper we give a new proof of Harnack’s inequality for elliptic operator in divergence form. We imitate the proof given by Caffarelli for operators in nondivergence form.

In this article, we prove some weighted pointwise estimates for three discontinuous Galerkin methods with lifting operators appearing in their corresponding bilinear forms. We consider a Dirichlet problem with a general second order elliptic operator.

Let L be a second order elliptic differential operator on a Riemannian manifold E with no zero order terms. We say that a function h is L-harmonic if Lh = 0. Every positive L-harmonic function has a unique representation

Let R 2 be a bounded domain with Lipschitz boundary and let : ! R be a function which is measurable and bounded away from zero and innnity. We consider the divergence form elliptic operator

We study here a class of quasilinear elliptic systems involving the p-Laplacian operator. Under some suitable assumptions on the nonlinearities, we show the existence result by using a fixed point theorem.

We study the numerical solution of a Cauchy problem for a self-adjoint elliptic partial differential equation uzz − Lu = 0 in three space dimensions (x, y, z) , where the domain is cylindrical in z. Cauchy data are given on the lower boundary and the boundary values on the upper boundary are sought. The problem is severely ill-posed. The formal solution is written as a hyperbolic cosine functio...

We compare various topologies on the space of (possibly unbounded) Fredholm selfadjoint operators and explain their K-theoretic relevance.∗ Introduction The work of Atiyah and Singer on the index of elliptic operators on manifolds has singled out the role of the space of bounded Fredholm operators in topology. It is a classifying space for a very useful functor, the topological K-theory. This m...

We study the convergence properties of the solutions of some elliptic obstacle problems with measure data, under the simultaneous perturbation of the operator, the forcing term and the obstacle. Stability results for obstacle problems with measure data 1

We study the existence and the properties of solutions to the Dirichlet problem for uniformly elliptic second-order Hamilton-JacobiBellman operators, depending on the principal eigenvalues of the operator.