Related papers: Local Sobolev-Poincare imbedding domains

Local-order-invariant (first-order) logic is an extension of first-order logic where formulae have access to a ternary local order relation on the Gaifman graph, provided that the truth value does not depend on the specific order relation…

We prove that for a domain $\Omega \subset \mathbb{R}^n$, being $(\epsilon,\delta)$ in the sense of Jones is equivalent to being an extension domain for bmo$(\Omega)$, the nonhonomogeneous version of the space of function of bounded mean…

We propose a new method for obtaining Poincare-type inequalities on arbitrary convex bodies in R^n. Our technique involves a dual version of Bochner's formula and a certain moment map, and it also applies to some non-convex sets. In…

We prove a local $L^p$-Poincar\'e inequality, $1\leq p < \infty$, on noncompact Lie groups endowed with a sub-Riemannian structure. We show that the constant involved grows at most exponentially with respect to the radius of the ball, and…

Denote by $ {\bf\dot B}^{\alpha,\phi}(\Omega)$ the Orlicz-Besov space, where $\alpha\in\mathbb{R}$, $\phi$ is a Young function and $\Omega\subset\mathbb{R}^n$ is a domain. For $\alpha\in(-n,0)$ and optimal $\phi$, in this paper we…

We establish the existence and uniqueness of the solution to the Dirichlet problem for the variable exponent $p$-Laplacian on a bounded, smooth domain $\Omega \subset {\mathbb R}^n$, where the boundary datum belongs to $W^{1,p}(\Omega)$.…

We characterize the real interpolation space between a weighted $L^p$ space and a weighted Sobolev space in arbitrary bounded domains in $\mathbb{R}^n$, with weights that are positive powers of the distance to the boundary.

A well-known result is that any Lipschitz domain is an extension domain for $W^{s,p}$. This paper extends this result to Lipschitz subsets of compact Lipschitz submanifolds of $\mathbb{R}^n$. We adapt the construction of an extension…

Let B be a commutative $\mathbb{Z}$-graded domain of characteristic zero. An element f of B is said to be cylindrical if it is nonzero, homogeneous of nonzero degree, and such that $B_{(f)}$ is a polynomial ring in one variable over a…

We define a notion of compressed local Artinian ring that does not require the ring to contain a field. Let $(R,\mathfrak m)$ be a compressed local Artinian ring with odd top socle degree $s$, at least five, and $\operatorname{socle}(R)\cap…

We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish…

Within the setting of metric spaces equipped with a doubling measure and supporting a $p$-Poincar\'e inequality, establishing existence of solutions to Dirichlet problem in a bounded domain in such a metric space is accomplished via direct…

It is well known that derivatives of solutions to elliptic boundary value problems may become unbounded near the corner of a domain with a conical singularity, even if the data are smooth. When the corner domain is approximated by more…

A pseudo independent (PI) model is a probabilistic domain model (PDM) where proper subsets of a set of collectively dependent variables display marginal independence. PI models cannot be learned correctly by many algorithms that rely on a…

A commutative integral domain is primary if and only if it is one-dimensional and local. A domain is strongly primary if and only if it is local and each nonzero principal ideal contains a power of the maximal ideal. Hence one-dimensional…

Let D be a bounded planar C^1 domain, or a Lipschitz domain "flat enough", and consider the Beurling transform of 1_D, the characteristic function of D. Using a priori estimates, in this paper we solve the following free boundary problem:…

We investigate distortion estimates for mappings at boundary points of a domain. We consider mappings of the Sobolev and Orlicz-Sobolev classes and some other classes of mappings that do not preserve the boundary of a domain. For above…

Let M be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue \lambda. We give upper and lower bounds on the inner radius of the type C/\lambda^k. Our proof is based on a local behavior of…

We give a direct proof of an important result of Solynin which says that the Poincar\'e metric is a strongly submultiplicative domain function. This result is then used to define a new capacity for compact subsets of the complex plane…

It is given a canonical representation of prime ends in regular spatial domains and, on this basis, it is studied the boundary behavior of the so-called lower Q-homeomorphisms that are the natural generalization of the quasiconformal…