相关论文: Fractional Sobolev norms and BV functions on manif…
We prove compactness of the embeddings in Sobolev spaces for fractional super and sub harmonic functions with radial symmetry. The main tool is a pointwise decay for radially symmetric functions belonging to a function space defined by…
In this paper, we study a family of general fractional Sobolev spaces $\MsqpOm$ when $\Om=\Rn$ or $\Om$ is a bounded domain, having a compact, Lipschitz boundary $\Bdy$, in $\Rn$ for $n\geq2$. Among other results, some compact embedding…
We study the boundary traces of Newton-Sobolev, Hajlasz-Sobolev, and BV (bounded variation) functions. Assuming less regularity of the domain than is usually done in the literature, we show that all of these function classes achieve the…
In this paper we establish weak continuity results for the distribution Jacobian minors in fractional sobolev spaces, which can be seen as a extension of recent work of Brezis and Nguyen on the distributional Jacobian determinant. Then we…
It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in $\mathbb{R}^n$, continue to be valid on a wide class of Riemannian manifolds with…
We study the regularity of local minimisers of a prototypical free-discontinuity problem involving both a manifold-valued constraint on the maps (which are defined on a bounded domain $\Omega \subset \R^2$) and a variable-exponent growth in…
We consider a family of non-local and non-convex functionals, and we prove that their Gamma-liminf is bounded from below by a positive multiple of the Sobolev norm or the total variation. As a by-product, we answer some open questions…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special…
For systems of ordinary differential equations on a compact interval, we study the character of solvability of the most general linear boundary-value problems in Sobolev spaces. We find the indices of these problems and obtain a criterion…
We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms $G_p: T_pM \to [0,\infty]$ are given. When we consider sub-Riemannian manifolds, our definition coincide with…
Apart from an account of classical preliminaries, this volume contains a systematic introduction to Sobolev spaces and functions of bounded variation with selected applications. This is installment III of a four part discussion of certain…
We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Compared with previous works, we consider more general functionals.…
Homogenization of integral functionals is studied under the constraint that admissible maps have to take their values into a given smooth manifold. The notion of tangential homogenization is defined by analogy with the tangential…
We investigate the form of the closure of the smooth, compactly supported functions $C_{c}^{\infty}(\Omega)$ in the weighted fractional Sobolev space $W^{s,p;\,w,v}(\Omega)$ for bounded $\Omega$. We focus on the weights $w,\,v$ being powers…
A novel representation is developed as a measure for multilinear fractional embedding. Corresponding extensions are given for the Bourgain-Brezis-Mironescu theorem and Pitt's inequality. New results are obtained for diagonal trace…
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…
In the setting of finite-dimensional $\mathrm{RCD}(K,N)$ spaces, we characterize the $p$-Sobolev spaces for $p\in(1,\infty)$ and the space of functions of bounded variation in terms of the short-time behaviour of the heat flow. Moreover, we…
Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes.…
We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.
We obtain a Bourgain-Br\'ezis-Mironescu formula on the limit behaviour of a modified fractional Sobolev seminorm when $s\nearrow 1$, which is valid in arbitrary bounded domains. In the case of extension domains, we recover the classical…