Related papers: Bounds for the volume of the solutions to a system…

We consider variational problems with regular H{\"o}lderian weight or boundary singularity, and Dirichlet condition. We prove the boundedness of the volume of the solutions to these equations on analytic domains.

We consider variational problems with regular H{\"o}lderian weight or with weight and boundary singularity and, Dirichlet condition. We prove the boundedness of the volume of the solutions to these equations on the annulus.

We give blow-up behavior for solutions to an elliptic system with Dirichlet condition, and, weight and boundary singularity. Also, we have a compactness result for this elliptic system with regular H{\"o}lderian weight and boundary…

We prove existence and regularity of solutions to degenerate and singular elliptic free boundary problems, where the volume of the positivity set of the solution is prescribed.

We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…

We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in $M\times \mathbb R_+$, where $M$ is a complete noncompact Riemannian manifold. Under specific assumptions, we establish…

In this short note, we consider the Dirichlet problem associated to an even order elliptic system with antisymmetric first order potential. Given any continuous boundary data, we show that weak solutions are continuous up to boundary.

Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness of their solutions is established…

We obtain bounded for all $t$ solutions of ordinary differential equations as limits of the solutions of the corresponding Dirichlet problems on $(-L,L)$, with $L \rightarrow \infty$. We derive a priori estimates for the Dirichlet problems,…

Under structural conditions which are almost optimal, we derive a quantitative version of boundary estimate then prove existence of solutions to Dirichlet problem for a class of fully nonlinear elliptic equations on Hermitian manifolds.

Gradient boundedness up to the boundary for solutions to Dirichlet and Neumann problems for elliptic systems with Uhlenbeck type structure is established. Nonlinearities of possibly non-polynomial type are allowed, and minimal regularity on…

We use an iteration procedure propped up by a a classical form of the maximum principle to show the existence of solutions to a nonlinear Poisson equation with Dirichlet boundary conditions. These methods can be applied to the case of…

We prove some upper bounds for the Dirichlet eigenvalues of a class of fully nonlinear elliptic equations, namely the Hessian equations

This paper investigates the relation between the boundary geometric properties and the boundary regularity of the solutions of elliptic equations. We prove by a new unified method the pointwise boundary H\"{o}lder regularity under proper…

The purpose of this article is to study extrapolation of solvability for boundary value problems of elliptic systems in divergence form on the upper half-space assuming De Giorgi type conditions. We develop a method allowing to treat each…

Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem has a positive solution, then it is bounded…

This work deals with the system $(-\Delta)^m u= a(x) v^p$, $(-\Delta)^m v=b(x) u^q$ with Dirichlet boundary condition in a domain $\Omega\subset\RR^n$, where $\Omega$ is a ball if $n\ge 3$ or a smooth perturbation of a ball when $n=2$. We…

We establish existence and multiplicity of solutions for a elliptic resonant elliptic problem under Dirichlet boundary conditions.

We establish several results related to existence, nonexistence or bifurcation of positive solutions for a Dirichlet boundary value problem with in a smooth bounded domain. The main feature of this paper consists in the presence of a…

In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…