Related papers: Second-order estimates for the $p$-Laplacian in RC…

Let $n \ge 2$ and $\Omega \subset \mathbb{R}^n$ be a bounded Lipschitz domain. In this article, we establish first-order global regularity estimates in the scale of BMO spaces on $\Omega$ for weak solutions to the second-order elliptic…

In this paper we consider Sobolev inequalities associated with singular problems for the fractional $p$-Laplacian operator in a bounded domain of $\mathbb{R}^{N}$, $N\geq 2$.

Let $M$ be an $n$-dimensional closed orientable submanifold in an $N$-dimensional space form. When $1<p \le \frac n2 + 1$, we obtain an upper bound for the first nonzero eigenvalue of the $p$-Laplacian in terms of the mean curvature of $M$…

In this paper we investigate the validity of first and second order $L^{p}$ estimates for the solutions of the Poisson equation depending on the geometry of the underlying manifold. We first present $L^{p}$ estimates of the gradient under…

We obtain Calder\'on-Zygmund type estimates in generalized Morrey spaces for nonlinear equations of $p$-Laplacian type. Our result is obtained under minimal regularity assumptions both on the operator and on the domain. This result allows…

We study doubly nonlinear parabolic equation arising from the gradient flow for p-Sobolev type inequality, referred as p-Sobolev flow from now on, which includes the classical Yamabe flow on a bounded domain in Euclidean space in the…

In this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDE's around nonsmooth domains, essentially either Lipschitz or convex, or satisfying a uniform…

We show that the Dirichlet problem at infinity is unsolvable for the p-Laplace equation for any nonconstant continuous boundary data, for certain range of p>n, on an n-dimensional Cartan-Hadamard manifold constructed from a complete…

In this paper we develop the Perron method for solving the Dirichlet problem for the analog of the p-Laplacian, i.e. for p-harmonic functions, with Mazurkiewicz boundary values. The setting considered here is that of metric spaces, where…

On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…

Let D be a bounded domain in n-dimensional Euclidean space, where n>2, and let 1<p< (2n)/(n-2). We prove a reverse-Holder inequality for functions realizing equality in the Sobolev inequality, which finds a lower bound for their (p-1)-norm…

We establish L^p bounds on L^2 normalized spectral clusters for self-adjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all p between $2 and infinity, up to logarithmic losses…

In this paper we obtain symmetry and monotonicity results for positive solutions to some $p$-Laplacian cooperative systems in bounded domains involving first order terms and under zero Dirichlet boundary condition.

In this paper we study variations of the first non-trivial eigenvalues of the two-dimensional $p$-Laplace operator, $p>2$, generated by measure preserving quasiconformal mappings $\varphi : \mathbb D\to\Omega$, $\Omega \subset\mathbb R^2$.…

In the first part of this paper, we prove local interior and boundary gradient estimates for p-harmonic functions on general Riemannian manifolds. With these estimates, following the strategy in recent work of R. Moser, we prove an…

We consider the mixed Dirichlet-conormal problem on irregular domains in $\mathbb{R}^d$. Two types of regularity results will be discussed: the $W^{1,p}$ regularity and a non-tangential maximal function estimate. The domain is assumed to be…

This paper concerns the concentration of Dirichlet eigenfunctions of the Laplacian on a compact two-dimensional Riemannian manifold with strictly geodesically concave boundary. We link three inequalities which bound the concentration in…

Over the last years, minimization problems over spaces of measures have received increased interest due to their relevance in the context of inverse problems, optimal control and machine learning. A fundamental role in their numerical…

Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Lata{\l}a we provide a concentration inequality for non-necessarily Lipschitz functions $f\colon \R^n \to \R$ with bounded…

We prove Liouville type theorems for $p$-harmonic functions on exterior domains of the $d$-dimensional Euclidean space, where $1<p<\infty$ and $d\geq 2$. We show that every positive $p$-harmonic function satisfying zero Dirichlet, Neumann…