相关论文: Korn inequality on irregular domains

The paper is concerned with sharp estimates of constants in Poincare type inequalities for functions having zero mean value on the boundary of a Lipschitz domain or on a measurable part of it. These estimates are useful for various…

We study the best possible constants in Korn-type inequalities and their connection with Morrey's problem in the calculus of variations. We adapt techniques from the analysis of the Beurling-Ahlfors transform to Korn's inequality. In…

In this paper we prove an asymptotically sharp Bernstein-type inequality for polynomials on analytic Jordan arcs. Also a general statement on mapping of a domain bounded by finitely many Jordan curves onto a complement to a system of the…

In this paper we establish a new class of weighted Hardy-Sobolev type inequalities under mild monotonicity assumptions on the weight function. As a consequence, we derive the corresponding weighted Sobolev and trace-type inequalities. These…

We prove boundary inequalities in arbitrary bounded Lipschitz domains on the trace space of Sobolev spaces. For that, we make use of the trace operator, its Moore-Penrose inverse, and of a special inner product. We show that our trace…

In this paper, we prove a class of weighted isoperimetric inequalities for bounded domains in hyperbolic space by using the isoperimetric inequality with log-convex density in Euclidean space. As a consequence, we remove the horo-convex…

In this paper we prove that if $\Omega\in\mathbb{R}^n$ is a bounded John domain, the following weighted Poincare-type inequality holds: $$ \inf_{a\in \mathbb{R}}\| (f(x)-a) w_1(x) \|_{L^q(\Omega)} \le C \|\nabla f(x) d(x)^\alpha w_2(x)…

In this work we prove some Hardy-Poincar\'{e} inequalities with quadratic singular potentials localized on the boundary of a smooth domain. Then, we consider conical domains with vertex on the singularity and we show upper and lower bounds…

We prove second and fourth order improved Poincar\'e type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as…

In this paper, we study the sharp Poincar\'e inequality and the Sobolev inequalities in the higher order Lorentz--Sobolev spaces in the hyperbolic spaces. These results generalize the ones obtained in \cite{Nguyen2020a} to the higher order…

The central aim of this paper is to study (regional) fractional Poincar\'e type inequalities on unbounded domains satisfying the finite ball condition. Both existence and non existence type results are established depending on various…

A form of Sobolev inequalities for the symmetric gradient of vector-valued functions is proposed, which allows for arbitrary ground domains in $\mathbb R ^n$. In the relevant inequalities, boundary regularity of domains is replaced with…

In this paper we give explicit examples of bounded domains that satisfy the quasihyperbolic boundary condition and calculate the values for the constants. These domains are also John domains and we calculate John constants as well. The…

The purpose of this paper is to construct a new class of discrete generalized Korn's inequalities for piecewise H2 vector fields in three-dimensional space. The resulting Korn's inequalities are different from the standard Korn's…

We study a weak formulation of Serrin's overdetermined boundary value problem in planar Jordan domains with rectifiable boundary. Our first result establishes that, within the class of rectifiable Jordan Smirnov domains, the corresponding…

We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.

In this paper, we explore carrot John domains within variational problems, dividing our examination into two distinct sections. The initial part is dedicated to establishing the lower semicontinuity of the (optimal) John constant concerning…

Necessary and sufficient conditions are exhibited for a Korn type inequality to hold between (possibly different) Orlicz norms of the gradient of vector-valued functions and of the deviatoric part of their symmetric gradients. As a…

In this paper we study two different weighted isoperimetric inequalities. In the first part of the paper we prove a sharp stability result for the isoperimetric inequality with a log-convex weight. In the second part we analize the behavior…

We study second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions. We prove existence and uniqueness of weak solutions and their continuity up to the boundary of…