相关论文: The Sobolev Jordan-Schonflies Problem

The manuscript is devoted to the boundary behavior of mappings with bounded and finite distortion, which has been actively studied recently. We consider mappings of domains of the Euclidean space that satisfy the inverse Poletsky inequality…

We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobolev functions. We study the dependence of the operator, its…

In the first part of this article we deal with the existence of at least three non-trivial weak solutions of a nonlocal problem with nonstandard growth involving a nonlocal Robin type boundary condition. The second part of the article is…

The main result of the present paper, combined with earlier results of Hardt and Lin settles the extension problem for $W^{1,p}(\mathcal M, \mathcal N)$, where $\mathcal M$ and $\mathcal N$ are compact riemannian manfolds, $\mathcal M$…

The classical Dirichlet problem for a second-order strongly elliptic system with constant coefficients in a Jordan domain is considered. We show that the solution of the problem can be represented as a functional series in powers of the…

The question is addressed of when a Sobolev type space, built upon a general rearrangement-invariant norm, on an $n$-dimensional domain, is a Banach algebra under pointwise multiplication of functions. A sharp balance condition among the…

In this paper we first introduce an innovative equivalent norm in the Musielak-Orlicz Sobolev spaces in a very general setting and we then present a new result on the boundedness of the solutions of a wide class of nonlinear Neumann…

We show that Sobolev space $W^1_1(\Omega)$ of any planar one-connected domain $\Omega$ has the Bounded Approximation property. The result holds independently from the properties of the boundary of $\Omega$. The prove is based on a new…

In this paper we study a Schr\"odinger-Bopp-Podolsky system of partial differential equations in a bounded and smooth domain of $\mathbb R^3$ with a non constant coupling factor. Under a compatibility condition on the boundary data we…

In this work, a mixed problem for a time-fractional equation with a delayed argument and pseudodifferential operators related to Laplace operators with non-local boundary conditions in Sobolev classes is studied. The solutions to the…

We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function $f\in L^p$ with $p>1$, i.e. bi-Sobolev solutions for the prescribed Jacobian inequality in the plane for right-hand sides $f\in…

It is proved the existence of nonclassical solutions of the Neumann problem for the harmonic functions in the Jordan rectifiable domains with arbitrary measurable boundary distributions of normal derivatives. The same is stated for the…

We extend Federer's coarea formula to mappings $f$ belonging to the Sobolev class $W^{1,p}(R^n;R^m)$, $1 \le m < n$, $p>m$, and more generally, to mappings with gradient in the Lorentz space $L^{m,1}(R^n)$. This is accomplished by showing…

Over a field of characteristic $0$ we give a concrete, computation--ready description of Jordan algebra structures and their low--order deformation theory. The Jordan identity is quartic in the elements and cubic in the multiplication, and…

We show a weighted version of Korn inequality on bounded euclidean John domains, where the weights are nonnegative powers of the distance to the boundary. In this theorem, we also provide an estimate of the constant involved in the…

Let $\Omega$ be an internal chord-arc Jordan domain and $\varphi:\mathbb S\rightarrow\partial\Omega$ be a homeomorphism. We show that $\varphi$ has finite dyadic energy if and only if $\varphi$ has a diffeomorphic extension $h: \mathbb…

We transfer the celebrating Monge-Kontorovich problem in a bounded domain of Euclidean plane into a Dirichlet boundary problem associated to a quasi-linear elliptic equation with $0-$order term missing in its diffusion coefficients:…

In this paper, we extend the fractional Sobolev spaces with variable exponents $W^{s,p(x,y)}$ to include the general fractional case $W^{K,p(x,y)}$, where $p$ is a variable exponent, $s\in (0,1)$ and $K$ is a suitable kernel. We are…

We prove a version of Smirnov type theorem and Charatheodory type theorem for a harmonic homeomorphism of the unit disk onto a Jordan surface with rectifiable boundary. Further we establish the classical isoperimetric inequality and…

This paper concerns positive solutions to the boundary value problems of the scalar field equation in the half space with a Sobolev supercritical nonlinearity and an inhomogeneous Dirichlet boundary condition, admitting a nontrivial…