Related papers: Local boundedness for weak solutions to some quasi…
By virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in…
We prove a comparison principle for local weak solutions to a class of widely degenerate elliptic equations of the form \begin{equation} -\text{div} \left( \left(|Du|-1 \right)^{p-1}_+\frac{Du}{|Du|} \right) = f(x,u) \qquad \text{ in }…
We develop regularity theory for degenerate elliptic equations with the degeneracy controlled by a weight. More precisely, we show local boundedness and continuity of weak solutions under the assumption of a weighted Orlicz-Sobolev and…
We discuss the existence and non-existence of non-negative weak solutions for second order nonlocal elliptic systems subject to functional boundary conditions. Our approach is based on classical fixed point index theory combined with some…
We establish a gradient estimate for a very weak solution to a quasilinear elliptic equation with a nonstandard growth condition, which is a natural generalization of the $p$-Laplace equation. We investigate the maximum extent for the…
Let $2 \le N\in\mathbb{N}$, $\Omega$ be a bounded open in $\mathbb{R}^{N}$, $T\in (0,\infty)$, $Q=\Omega\times (0,T)$, $u$ be a weak solution of parabolic equation $\displaystyle \frac{\partial u}{\partial t} -Lu= f$, where $L$ is an…
This paper deals with an existence and uniqueness result of the weak solution for a quasilinear elliptic PDE with nonlinear Robin boundary conditions.This problem is defined on a domain whose boundary is the union of two disjoint…
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.
The problem of characterizing weak limits of sequences of solutions for a non-linear diffusion equation of $p$-laplacian type is addressed. It is formulated in terms of certain moments of underlying Young measures associated with main…
In this paper we provide a local well posedness result for a quasilinear beam-wave system of equations on a one-dimensional spatial domain under periodic and Dirichlet boundary conditions. This kind of systems provides a refined model for…
We consider a kind of nonlinear systems on a locally finite graphs $G=(V,E)$. We prove via the mountain pass theorem that this kind of systems has a nontrivial ground state solution which depends on the parameter $\lambda$ with some…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…
In this paper, we analyze the existence of solution for a fractional elliptic system coupled by critical nonlinearities and endowed with mixed Dirichlet-Neumann boundary conditions. By means of variational methods and an…
We investigate the quasilinear elliptic system $-\Delta_{m} u&=u^{-p}v^{-q}$, $u>0 \quad\mbox{ in } \Omega$, $-\Delta_{m} v&=u^{r}v^{-s}$, $v>0 \quad\mbox{ in }\Omega$, $u=v=0 \quad\mbox{ on } \partial{\Omega}$, where $\Omega…
This paper concerns a time-independent thermoelectric model with two different boundary conditions. The model is a nonlinear coupled system of the Maxwell equations and an elliptic equation. By analyzing carefully the nonlinear structure of…
We prove a general result on the existence of local solutions of any second order quasi-linear elliptic system with arbitrary 1-jet at a point.
Motivated by problems arising in geometric flows, we prove several regularity results for systems of local and nonlocal equations, adapting to the parabolic case a neat argument due to Caffarelli. The geometric motivation of this work comes…
The existence of entire solutions to quasilinear elliptic systems exhibiting both singular and convective reaction terms is discussed. An auxiliary problem, obtained by `freezing' the convection terms and `shifting' the singular ones, is…
We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…
The purpose of this note is to study the weak solutions to the inviscid quasi-geostrophic system for initial data belonging to Lebesgue spaces. We give a global existence result as well as detail the connections between several different…