相关论文: Neumann problems for $p$-harmonic functions, and i…
We investigate the existence of nonnegative solutions for a nonlinear problem involving the fractional p-Laplacian operator. The problem is set on a unbounded domain, and compactness issues have to be handled.
This work is about global H\"older regularity for solutions to elliptic partial differential equations subject to mixed boundary conditions on irregular domains. There are two main results. In the first, we show that if the domain of the…
In this article, the problems to be studied are the following \leqnomode \begin{equation*} \label{p} \left\{\begin{array}{ll} (-\Delta )_p^s u \pm \dfrac{|u|^{p-2}u}{|x|^{sp}} = \lambda f(x,u) & \quad \mbox{in }\ \Omega\\[0.3cm] u= 0 &…
In this paper, we study the following Dirichlet problem for a parabolic equation involving fractional $p$-Laplacian with logarithmic nonlinearity \begin{equation*}\label{eq}\left\{ \begin{array}{llc}…
This paper is devoted to considering the following Hardy-Sobolev inequality \[ \int_{\mathbb{R}^N}|\nabla u|^p \mathrm{d}x \geq \mathcal{S}_\beta\left(\int_{\mathbb{R}^N}\frac{|u|^{p^*_\beta}}{|x|^{\beta}}…
We give an alternative proof for H\"older regularity for weak solutions of nonlocal elliptic quasilinear equations modelled on the fractional p-Laplacian where we replace the discrete De Giorgi iteration on a sequence of concentric balls by…
Under simple hypotheses on the nonlinearity $f$, we consider the fractional harmonic operator problem \begin{equation}\label{abstr}\sqrt{-\Delta+|x|^2}\,u=f(x,u)\ \ \textrm{in }\ \mathbb{R}^N\end{equation} or, since we work in the extension…
We prove fractional Sobolev-Poincar\'e inequalities, capacitary versions of fractional Poincar\'e inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results…
Within the framework of Hilbert spaces, we solve nonlocal problems in bounded domains with prescribed conditions on the complement of the domain. Our main focus is on the inhomogeneous Neumann problem in a rather general setting. We also…
We introduce the notion of a regular mapping on a non-commutative $L_p$-space associated to a hyperfinite von Neumann algebra for $1\le p\le \infty$. This is a non-commutative generalization of the notion of regular or order bounded map on…
The primary purpose of this paper is to study the Wiener-type regularity criteria for non-linear equations driven by integro-differential operators, whose model is the fractional $p-$Laplace equation. In doing so, with the help of tools…
We study the fractional $p$-Laplace equation $$ (-\Delta_p)^s u = 0 $$ for $0<s<1$ and in the subquadratic case $1<p<2$. We provide H\"older estimates with an explicit H\"older exponent. The inhomogeneous equation is also treated and there…
We prove the equivalence of Hardy- and Sobolev-type inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean…
We introduce n/p-harmonic maps as critical points of E(v) the Lp-Norm of the alpha-laplacian of v, where pointwise v maps Rn into a sphere, and alpha = n/p. This energy combines the non-local behaviour of the fractional harmonic maps…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
In [KP16] (arXiv:1605.07880) the authors introduced a second-order variational problem in $L^{\infty}$. The associated equation, coined the $\infty$-Bilaplacian, is a \emph{third order} fully nonlinear PDE given by $\Delta^2_\infty u\, :=…
We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions. For the fractional $p$-Laplace operator it implies that solutions to certain degenerate nonlocal equations are higher…
In this paper we consider a fractional $p$-Laplacian equation in the entire space $\mathbb{R}^{N}$ with doubly critical singular nonlinearities involving a local critical Sobolev term together with a nonlocal Choquard critical term; the…
By virtue of barrier arguments we prove $C^\alpha$-regularity up to the boundary for the weak solutions of a non-local nonlinear problem driven by the fractional $p$-Laplacian operator. The equation is boundedly inhomogeneous and the…
We study regularity properties of solutions to nonlinear and nonlocal evolution problems driven by the so-called \emph{$0$-order fractional $p-$Laplacian} type operators: $$ \partial_t u(x,t)=\mathcal{J}_p u(x,t):=\int_{\mathbb{R}^n}…