Related papers: The complement value problem for a class of second…

We develop an elliptic theory based in $L^2$ of boundary value problems for general wedge differential operators of first order under only mild assumptions on the boundary spectrum. In particular, we do not require the indicial roots to be…

We study a mixed boundary value problem for the quasilinear elliptic equation $\mathop{\rm div}\mathcal{A}(x,\nabla u(x))=0$ in an open infinite circular half-cylinder with prescribed continuous Dirichlet data on a part of the boundary and…

In this paper, authors shall introduce a finite element method by using a weakly defined gradient operator over discontinuous functions with heterogeneous properties. The use of weak gradients and their approximations results in a new…

We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D=divpgrad+q in the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the…

This paper is concerned with the Dirichlet problem for an equation involving the 1--Laplacian operator $\Delta_1 u$ and having a singular term of the type $\frac{f(x)}{u^\gamma}$. Here $f\in L^N(\Omega)$ is nonnegative, $0<\gamma\le1$ and…

We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators…

In this paper the discrete eigenvalues of elliptic second order differential operators in $L^2(\mathbb{R}^n)$, $n \in \mathbb{N}$, with singular $\delta$- and $\delta'$-interactions are studied. We show the self-adjointness of these…

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…

Let $\Omega $ be a bounded domain in $\mathbb{R}^{d}$ $\left( d\geq 2\right) $ pretty regular. We solve the variational Dirichlet problem for a class of quasi-linear elliptic systems.

In this paper, we prove a higher integrability result for very weak solutions of higher-order elliptic systems involving a double phase operator as the principal part. As a model case, we consider \begin{equation} \int_{\Omega} \left( |D^m…

We deal with boundary value problems for second-order nonlinear elliptic equations in divergence form, which emerge as Euler-Lagrange equations of integral functionals of the Calculus of Variations built upon possibly anisotropic norms of…

In this study, we devote our attention to the question of clarifying the existence of a weak solution to a class of quasilinear double-phase elliptic equations with logarithmic convection terms under some appropriate assumptions on data.…

In this paper we introduce an integer-valued degree for second order fully nonlinear elliptic operators with nonlinear oblique boundary conditions. We also give some applications to the existence of solutions of certain nonlinear elliptic…

A sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity properties of solutions to nonlinear elliptic…

We give necessary and sufficient conditions for the existence of weak solutions to the model equation $$-\Delta_p u=\sigma \, u^q \quad \text{on} \, \, \, \R^n,$$ in the case $0<q<p-1$, where $\sigma\ge 0$ is an arbitrary locally integrable…

In this article we provide existence, uniqueness and regularity results of a degenerate singular elliptic boundary value problem whose prototype is given by \begin{gather*} \begin{cases} -\operatorname{div}(w(x)|\nabla u|^{p-2}\nabla…

Let $n\geq2$ and $ \Omega\subset \mathbb{R}^{n+1}$ be a Lipschitz wedge- like domain . We construct positive weak solutions of the problem $$\Delta u + u^p = 0 \quad\hbox{in}\, \Omega,$$ which vanish in a suitable trace sense on…

We consider a boundary value problem involving conformable derivative of order $\alpha ,$ $1<\alpha <2$ and Dirichlet conditions. To prove the existence of solutions, we apply the method of upper and lower solutions together with Schauder's…

For bounded domains $\Omega$ with Lipschitz boundary $\Gamma$, we investigate boundary value problems for elliptic operators with variable coefficients of fourth order subject to Wentzell (or dynamic) boundary conditions. Using form…

We obtain conditions for the differentiability of weak solutions for a second-order uniformly elliptic equation in divergence form with a homogeneous co-normal boundary condition. The modulus of continuity for the coefficients is assumed to…