Related papers: A compactness result for a Gelfand-Liouville syste…

This paper deals with the problem of finding bi-Lipschitz behavior in non-degenerate Lipschitz maps between metric measure spaces. Specifically, we study maps from (subsets of) Ahlfors regular PI spaces into sub-Riemannian Carnot groups. We…

We establish partial regularity result for vector-valued solutions to second order elliptic system in divergence form. The coefficients safisfies Dini condition respect to $(x,u)$ with growth order lager than 2. We prove $C^1$-regularity of…

In this paper, we prove a Serrin-type result for an elliptic system of equations, overdetermined with both Dirichlet and a generalized Neumann conditions. With this tool, we characterize the critical shapes under volume constraint of some…

In this paper, we prove an extrapolation result for complex coefficient divergence form operators that satisfy a strong ellipticity condition known as $p$-{\it ellipticity}. Specifically, let $\Omega$ be a chord-arc domain in $\mathbb R^n$…

In a cylindrical space-time domain with a convex, spatial base, we establish a local Lipschitz estimate for weak solutions to parabolic systems with Uhlenbeck structure up to the lateral boundary, provided homogeneous Dirichlet data are…

We give examples of systems of Partial Differential Equations that admit non-trivial, Lipschitz and one-homogeneous solutions in the form $u(R,\theta) = Rg(\theta)$, where $(R,\theta)$ are plane polar coordinates and $g: \mathbb{R}^{2} \to…

Lipschitz constants for the width and diameter functions of a convex body in $\mathbb R^n$ are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.

On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.

We establish local interior Lipschitz continuity of the solutions of a class of free boundary elliptic problems assuming the coefficients of the equation of Dini mean oscillation in at least one direction. The novelty in this regularity…

We prove existence and regularity results for weak solutions of non linear elliptic systems with non variational structure satisfying $(p,q)$-growth conditions. In particular we are able to prove higher differentiability results under a…

We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. Under the Lipschitz condition on the coefficients we characterize the domain of the Poisson operators…

We prove some Liouville-type theorems for stable solutions (and solutions stable outside a compact set) of quasilinear anisotropic elliptic equations. Our results cover the particular case of the pure Finsler p-Laplacian.

We prove an extension of Hoermander's classical result on hypoelliptic second order equations, where the coefficients of the related vector fields are globally Lipschitz and satisfy the classical Hoermander condition on a dense set while…

We establish the convergence of an adaptive spline-based finite element method of a fourth order elliptic problem with weakly-imposed Dirichlet boundary conditions using polynomial B-splines.

We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…

The objective of this paper is to establish a connection between the problem of optimal regularity among solutions to elliptic PDEs with measurable coefficients and the Liouville property at infinity. Initially, we address the…

This paper is devoted to present an approximation of a Cauchy problem for Friedrichs' systems under convex constraints. It is proved the strong convergence in L^2\_{loc} of a parabolic-relaxed approximation towards the unique constrained…

We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients $M=\Gamma\backslash G$ of a simply-connected solvable Lie group $G$ by a lattice $\Gamma$, admitting a symplectic structure.

We study $L^2$-constraint minimizing problems related to elliptic systems. We introduce a new rearrangement to show $H^1$-precompactness of any minimizing sequences. Some strict inequality for the new rearrangement is obtained. It is a key…

We establish the regularity in 2 dimensions of $L^2$ solutions to critical elliptic systems in divergence form involving involution operators of finite $W^{1,2}$-energy.