Related papers: Singular solutions for complex second order ellipt…

In this article, we improve the convergence order of some finite volume solutions approximating some second order elliptic problems. We prove that finite volume approximations of order $O(h^{k+1})$, with $k$ integer, can be obtained after…

Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the…

We consider solutions to degenerate anisotropic elliptic equations in order to study their regularity. In particular we establish second-order estimates and enclose regularity results for the stress field. All our results are new even in…

We propose a probabilistic definition of solutions of semilinear elliptic equations with (possibly nonlocal) operators associated with regular Dirichlet forms and with measure data. Using the theory of backward stochastic differential…

We prove estimates for weak solutions to a class of Dirichlet problems associated to anisotropic elliptic equations with a zero order term.

For a second-order elliptic equation of nondivergence form in the plane, we investigate conditions on the coefficients which imply that all strong solutions have first-order derivatives that are Lipschitz continuous or differentiable at a…

The paper concerns singular solutions of nonlinear elliptic equations.

In this paper, we deal with anisotropic singular perturbations of some class of elliptic problem. We study the asymptotic behavior of the solution in certain second order pseudo Sobolev space.

There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…

We consider the uniqueness of the following positive solutions of anisotropic elliptic equation: \begin{equation} \nonumber \left\{ \begin{aligned} -\Delta^F_p u&=u^q \quad \text{in} \quad \Omega, u&=0 \quad \text{on} \quad \partial \Omega,…

We obtain a local estimate for the gradient of solutions to a second-order elliptic equation in divergence form with bounded measurable coefficients that are square-Dini continuous at the single point x=0. In particular, we treat the case…

We establish $L^p$ solvability of the Dirichlet problem, for some finite $p$, in a 1-sided chord-arc domain $\Omega$ (i.e., a uniform domain with Ahlfors-David regular boundary), for elliptic equations of the form \[ Lu=-\text{div}(A\nabla…

We consider a non-uniformly elliptic second-order differential operator with periodic coefficients that models composite media consisting of highly anisotropic cylindrical fibres periodically distributed in an isotropic background. The…

Using a method developped in [1] and [2], we prove the existence of weak non trivial solutions to fourth order elliptic equations with singularities and with critical Sobolev growth.

We derive a priori second order estimates for solutions of a class of fully nonlinear elliptic equations on Riemannian manifolds under some very general structure conditions. We treat both equations on closed manifolds, and the Dirichlet…

Consider positive solutions to second order elliptic equations with measurable coefficients in a bounded domain, which vanish on a portion of the boundary. We give simple necessary and sufficient geometric conditions on the domain, which…

In this article we study the asymptotic behavior, of the solution of a nonlinear elliptic, anisotropic singular perturbations problem in cylindrical domain, the limit problem is given and strong convergences are proved, we also give an…

A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…

We provide a new result on the existence of extremal solutions for second-order Dirichlet problems with deviation argument. As a novelty in this work, the nonlinearity need not be continuous or monotone. In order to obtain this new result,…

We study the fully discrete elliptic integrable model Q4 and its immediate trigonometric and rational counterparts (Q3, Q2 and Q1). Singular boundary problems for these equations are systematised in the framework of global singularity…