Zobrazeno 1 - 10
of 241
pro vyhledávání: '"Shanmugalingam, Nageswari"'
We prove well-posedness, Harnack inequality and sharp regularity of solutions to a fractional $p$-Laplace non-homogeneous equation $(-\Delta_p)^su =f$, with $0
Externí odkaz:
http://arxiv.org/abs/2410.18883
In the context of a metric measure space $(X,d,\mu)$, we explore the potential-theoretic implications of having a finite-dimensional Besov space. We prove that if the dimension of the Besov space $B^\theta_{p,p}(X)$ is $k>1$, then $X$ can be decompos
Externí odkaz:
http://arxiv.org/abs/2409.01292
In this paper we consider the setting of a locally compact, non-complete metric measure space $(Z,d,\nu)$ equipped with a doubling measure $\nu$, under the condition that the boundary $\partial Z:=\overline{Z}\setminus Z$ (obtained by considering the
Externí odkaz:
http://arxiv.org/abs/2408.02624
We study the large-scale behavior of Newton-Sobolev functions on complete, connected, proper, separable metric measure spaces equipped with a Borel measure $\mu$ with $\mu(X) = \infty$ and $0 < \mu(B(x, r)) < \infty$ for all $x \in X$ and $r \in (0,
Externí odkaz:
http://arxiv.org/abs/2407.18315
In this note, we construct a Dirichlet-to-Neumann map, from a Besov space of functions, to the dual of this class. The Besov spaces are of functions on the boundary of a bounded, locally compact uniform domain equipped with a doubling measure support
Externí odkaz:
http://arxiv.org/abs/2403.06042
We give a sharp Hausdorff content estimate for the size of the accessible boundary of any domain in a metric measure space of controlled geometry, i.e., a complete metric space equipped with a doubling measure supporting a $p$-Poincar\'e inequality f
Externí odkaz:
http://arxiv.org/abs/2311.11960
Given a compact doubling metric measure space $X$ that supports a $2$-Poincar\'e inequality, we construct a Dirichlet form on $N^{1,2}(X)$ that is comparable to the upper gradient energy form on $N^{1,2}(X)$. Our approach is based on the approximatio
Externí odkaz:
http://arxiv.org/abs/2310.14436
Here we consider two notions of mappings of bounded variation (BV) from the metric measure space into the metric space; one based on relaxations of Newton-Sobolev functions, and the other based on a notion of AM-upper gradients. We show that when the
Externí odkaz:
http://arxiv.org/abs/2308.10353
We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "visibility" indicates the existence of John curves connecting the inte
Externí odkaz:
http://arxiv.org/abs/2308.09800
In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely $p$-integrable in the domain with a finite $p$. For continuous eikonal equations, it is known tha
Externí odkaz:
http://arxiv.org/abs/2308.06872