Related papers: On a Neumann problem for variational functionals o…

We prove that, any problem of minimization of proper lower semicontinuous function defined on a normal Hausdorff space, is canonically equivalent to a problem of minimization of a proper weak * lower semicontinuous convex function defined…

Analysis of non-compact manifolds almost always requires some controlled behavior at infinity. Without such, one neither can show, nor expect, strong properties. On the other hand, such assumptions restrict the possible applications and…

We provide a sufficient condition for the existence of a positive solution to $-\Delta u+V(|x|) u=u^p$ in $B_1$, when p is large enough. Here $B_1$ is the unit ball of $R^n$, n greater or equal to 2, and we deal both with Neumann and…

In this paper we consider the problem of minimizing functionals of the form $E(u)=\int_B f(x,\nabla u) \,dx$ in a suitably prepared class of incompressible, planar maps $u: B \rightarrow \mathbb{R}^2$. Here, $B$ is the unit disk and…

We study boundary value problems for bounded uniform domains in $\mathbb{R}^n$, $n\geq 2$, with non-Lipschitz (and possibly fractal) boundaries. We prove Poincar\'e inequalities with trace terms and uniform constants for uniform…

This paper is concerned with the Cauchy-Dirichlet problem for a doubly nonlinear parabolic equation involving variable exponents and provides some theorems on existence and regularity of strong solutions. In the proof of these results, we…

In this paper we study the asymptotic behaviour of the solutions of some minimization problems for integral functionals with convex integrands, in two-dimensional domains with cracks, under perturbations of the cracks in the Hausdorff…

The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…

We consider a class of integral functionals with Musielak-Orlicz type variable growth, possibly linear in some regions of the domain. This includes $p(x)$ power-type integrands with $p(x)\ge 1$ as well as double-phase $p\!-\!q$ integrands…

We study local regularity properties of local minimizer of scalar integral functionals of the form $$\mathcal F[u]:=\int_\Omega F(\nabla u)-f u\,dx$$ where the convex integrand $F$ satisfies controlled $(p,q)$-growth conditions. We…

We investigate regularity of minimizers in two dimensions for certain classes of non-smooth convex functionals. In particular our results apply to the surface tensions that appear in recent works on random surfaces and random tilings of…

We introduce variational problems on Riemannian manifolds with constrained acceleration and derive necessary conditions for normal extremals in the constrained variational problem. The problem consists on minimizing a higher-order energy…

We study the question whether Lipschitz minimizers of $\int F(\nabla u)\,dx$ in $\mathbb{R}^n$ are $C^1$ when $F$ is strictly convex. Building on work of De Silva-Savin, we confirm the $C^1$ regularity when $D^2F$ is positive and bounded…

In this paper we consider the existence and multiplicity of weak solutions for the following class of fractional elliptic problem \begin{equation}\label{00} \left\{\begin{aligned} (-\Delta)^{\frac{1}{2}}u + u &= Q(x)f(u)\;\;\mbox{in}\;\;\R…

We consider the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map. We begin with a negative…

We prove the uniqueness and nondegeneracy of least-energy solutions of a fractional Dirichlet semilinear problem in sufficiently large balls and in more general symmetric domains. Our proofs rely on uniform estimates on growing domains, on…

We study the Dirichlet problem for minimal surface systems in arbitrary dimension and codimension via mean curvature flow, and obtain the existence of minimal graphs over arbitrary mean convex bounded $C^2$ domains for a large class of…

We define a family of functionals, called p-oscillation functionals, that can be interpreted as discrete versions of the classical total variation functional for p=1 and of the p-Dirichlet functionals for p>1. We introduce the notion of…

We develop a variational approach to the minimization problem of functionals of the type $\frac12\left\lVert \nabla \phi \right\rVert^2_2 + \beta \left\lVert \phi \right\rVert_1$ constrained by $\left\lVert \phi \right\rVert_2 = 1$ which is…

The main goal of this article is to study a Calder\'on type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely determines on the one hand linear perturbations and on the…