Related papers: The variable exponent BV-Sobolev capacity

This paper proposes a mixed variational formulation for the problem of two coupled plates with a rigid {junction}. The proposed mixed {formulation} introduces {the union of} stresses and moments as {an auxiliary variable}, which {are}…

We obtain well-posedness results in $L_p$-based weighted Sobolev spaces for a transmission problem for anisotropic Stokes and Navier-Stokes systems with $L_{\infty}$ strongly elliptic coefficient tensor, in complementary Lipschitz domains…

We establish a Wiener-type integral condition for first-order Sobolev functions defined on a complete, doubling metric measure space supporting a Poincar\'e inequality. It is stronger than the Lebesgue point property, except for a marginal…

In this paper we study parabolic stochastic partial differential equations defined on arbitrary bounded domain $\cO \subset \bR^d$ allowing Hardy inequality: $$ \int_{\cO}|\rho^{-1}g|^2\,dx\leq C\int_{\cO}|g_x|^2 dx, \quad \forall g\in…

For the class of mixed channels decomposed into stationary memoryless channels, single-letter characterizations of the $\varepsilon$-capacity have not been known except for restricted classes of channels such as the regular decomposable…

The unique solvability of parabolic equations in Sobolev spaces with mixed norms is presented. The second order coefficients (except $a^{11}$) are assumed to be only measurable in time and one spatial variable, and VMO in the other spatial…

We study the Lp-properties of positive Rockland operators and define Sobolev spaces on general graded groups. This generalises the case of sub-Laplacians on stratified groups studied by G. Folland in [3]. We show that the defined Sobolev…

We construct and investigate the properties of tempered ultradistribution spaces in Sobolev spaces. A new Sobolev space preserving the original properties and condition whose derivatives are linear continuous operators embedding in $L^p$…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…

This paper has the characteristics of a review paper in which results of shift-invariant subspaces of Sobolev type are summarized without proofs. The structure of shift-invariant spaces $V_s$, $s\in\mathbb{R}$, generated by at most…

In this paper we study a non-homogeneous eigenvalue problem involving variable growth conditions and a potential $V$. The problem is analyzed in the context of Orlicz-Sobolev spaces. Connected with this problem we also study the…

We provide a new, short proof of the density in energy of Lipschitz functions into the metric Sobolev space defined by using plans with barycenter (and thus, a fortiori, into the Newtonian-Sobolev space). Our result covers first-order…

Let $\mathscr{C}_n=\{-1,1\}^n$ be the discrete hypercube equipped with the uniform probability measure $\sigma_n$. We prove that if $(E,\|\cdot\|_E)$ is a Banach space of finite cotype and $p\in[1,\infty)$, then every function…

We define and study Sobolev spaces associated with Jacobi expansions. We prove that these Sobolev spaces are isomorphic to Jacobi potential spaces. As a technical tool, we also show some approximation properties of Poisson-Jacobi integrals.

Let $f : U\subset\Rm \to \calQ_Q(\ell_2)$ be of Sobolev class $W^{1,p}$, $1 < p < \infty$. If $f$ almost minimizes its $p$ Dirichlet energy then $f$ is H\"older continuous. If $p=2$ and $f$ is squeeze and squash stationary then $f$ is in…

We introduce Hilbertian Hardy--Sobolev spaces on tube domains over convex cones and develop their structural theory from a Fourier-analytic point of view. We first establish a Paley--Wiener type representation, which identifies these spaces…

The first part of this paper surveys several results on the lattice structure of variable exponent Lebesgue function spaces (or Nakano spaces) $\lpv$. In the second part strictly singular and disjointly strictly singular operators between…

In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.

We apply a symmetrization procedure to the setting of Jacobi expansions and study potential spaces in the resulting situation. We prove that the potential spaces of integer orders are isomorphic to suitably defined Sobolev spaces. Among…

Formal series solutions and the Kovalevskaya exponents of a quasi-homogeneous polynomial system of differential equations are studied by means of a weighted projective space and dynamical systems theory. A necessary and sufficient condition…