Related papers: Global regularity for the $\bar\partial$-Neumann p…

This thesis deals with Partial Differential Equations in Several Complex Variables and especially focuses on a general estimate for the $\bar\partial$-Neumann problem on a domain which is $q$-pseudoconvex or $q$-pseudoconcave at a boundary…

We are interested in regularity properties of semi-stable solutions for a class of singular semilinear elliptic problems with advection term defined on a smooth bounded domain of a complete Riemannian manifold with zero Dirichlet boundary…

This paper is devoted to the investigation of the boundary regularity for the Poisson equation $${{cc} -\Delta u = f & \text{in} \Omega u= 0 & \text{on} \partial \Omega$$ where $f$ belongs to some $L^p(\Omega)$ and $\Omega$ is a…

In this paper we investigate the $L^p$ regularity, $L^p$ Neumann and $W^{1,p}$ problems for generalized Schr\"odinger operator $-\text{div}(A\nabla )+ V $ in the region above a Lipschitz graph under the assumption that $A$ is elliptic,…

We consider the existence of positive solutions to weighted quasilinear elliptic differential equations of the type \[ \begin{cases} - \Delta_{p, w} u = \sigma u^{q} & \text{in $\Omega$}, \\ u = 0 & \text{on $\partial \Omega$} \end{cases}…

Using a variational approach we study interior regularity for quasiminimizers of a $(p,q)$-Dirichlet integral, as well as regularity results up to the boundary, in the setting of a metric space equipped with a doubling measure and…

We present rigidity results for overdetermined problems associated to the rotationally invariant Poisson equation $-\Delta_{g_\mathcal{M}} u = f(r)$ in a model manifold $\mathcal{M} = [0,S) \times_h \mathbb S^{N-1}$ with warping function…

We prove improved differentiability results for relaxed minimisers of vectorial convex functionals with $(p, q)$-growth, satisfying a H\"older-growth condition in $x$. We consider both Dirichlet and Neumann boundary data. In addition, we…

In this paper, we study the minimization of $\lambda_{1}(\Omega)$, the first Dirichlet eigenvalue of the Laplace-Beltrami operator, within the class of open sets $\Omega$ of fixed volume in a Riemmanian manifold $(M,g)$. In the Euclidian…

Let $\Omega$ be a domain of $\mathbb R^n$ with $n\ge 2$ and $p(\cdot)$ be a local Lipschitz funcion in $\Omega$ with $1<p(x)<\infty$ in $\Omega$. We build up an interior quantitative second order Sobolev regularity for the normalized…

We consider the nonlinear Neumann problem for fully nonlinear elliptic PDEs on a quadrant. We establish a comparison theorem for viscosity sub and supersolutions of the nonlinear Neumann problem. The crucial argument in the proof of the…

In the article we study the Neumann $(p,q)$-eigenvalue problems in bounded H\"older $\gamma$-singular domains $\Omega_{\gamma}\subset \mathbb{R}^n$. In the case $1<p<\infty$ and $1<q<p^{*}_{\gamma}$ we prove solvability of this eigenvalue…

This work addresses the problem of (global) maximal regularity for quasilinear evolution equations with sublinear gradient growth and right-hand side in Lebesgue spaces, complemented with Neumann boundary conditions. The proof relies on a…

Given a conformally variational scalar Riemannian invariant $I$, we identify a sufficient condition for a compact Riemannian manifold to admit finite regular coverings with many nonhomothetic conformal rescalings with $I$ constant. We also…

Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide…

Given a formally integrable almost complex structure $X$ defined on the closure of a bounded domain $D \subset \mathbb C^n$, and provided that $X$ is sufficiently close to the standard complex structure, the global Newlander-Nirenberg…

We consider the problem of minimizing the Lagrangian $\int [F(\nabla u)+f\,u]$ among functions on $\Omega\subset\mathbb{R}^N$ with given boundary datum $\varphi$. We prove Lipschitz regularity up to the boundary for solutions of this…

We prove that the defocusing quintic wave equation, with Neumann boundary conditions, is globally wellposed on $H^1_N(\Omega) \times L^2(\Omega)$ for any smooth (compact) domain $\Omega \subset \mathbb{R}^3$. The proof relies on one hand on…

In this paper we investigate a forced incompressible Navier-Stokes equation coupled with a parabolic type equation of Q-tensors in a domain $U\subset\R^3.$ In the case $U$ is bounded, we prove the existence of a global strong solution when…

In this paper we prove that, given a compact four dimensional smooth Riemannian manifold (M,g) with smooth boundary there exists a metric conformal to g with constant T-curvature, zero Q-curvature and zero mean curvature under generic and…