Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Korobkov, Mikhail V."'
Let $p\ge 1$ and let $\mathbf v \colon \mathbb R^d \to \mathbb R^d$ be a compactly supported vector field with $\mathbf v \in L^p(\mathbb R^d)$ and $\operatorname{div} \mathbf v = 0$ (in the sense of distributions). It was conjectured by Nelson that
Externí odkaz:
http://arxiv.org/abs/2411.09338
A comprehensive theory of the effect of Orlicz-Sobolev maps, between Euclidean spaces, on subsets with zero or finite Hausdorff measure is offered. Arbitrary Orlicz-Sobolev spaces embedded into the space of continuous function and Hausdorff measures
Externí odkaz:
http://arxiv.org/abs/2208.08152
Autor:
Korobkov, Mikhail V., Ren, Xiao
In the celebrated paper by Jean Leray, published in JMPA journal in 1933, the invading domains method was proposed to construct D-solutions for the stationary Navier-Stokes flow around obstacle problem. In two dimensions, whether Leray's D-solution a
Externí odkaz:
http://arxiv.org/abs/2105.08898
We study the boundary value problem for the stationary Navier--Stokes system in two dimensional exterior domain. We prove that any solution of this problem with finite Dirichlet integral is uniformly bounded. Also we prove the existence theorem under
Externí odkaz:
http://arxiv.org/abs/1711.02400
Publikováno v:
Analysis & PDE 12 (2019) 1149-1175
We study Luzin N-property with respect to the Hausdorff measures for Sobolev spaces W^k_p(R^n,R^d). We prove that such N-property holds except for one critical dimensional value t_*=n-(k-1)p; for this critical value the N-property fails in general, a
Externí odkaz:
http://arxiv.org/abs/1706.04796
The classical Morse--Sard theorem claims that for a mapping $v:\mathbb R^n\to\mathbb R^{m+1}$ of class $C^k$ the measure of critical values $v(Z_{v,m})$ is zero under condition $k\ge n-m$. Here the critical set, or $m$-critical set is defined as $Z_{
Externí odkaz:
http://arxiv.org/abs/1706.05266
Publikováno v:
J. Funct. Anal. 272:3 (2017), 1265-1295
The Morse-Sard theorem requires that a mapping $v:R^n \to R^m$ is of class $C^k$, $k>n-m$. In 1957 Dubovitski\u{\i} generalized this result by proving that almost all level sets for a $C^k$ mapping have $H^s$-negligible intersection with its critical
Externí odkaz:
http://arxiv.org/abs/1603.05858
Publikováno v:
In Advances in Mathematics 6 January 2021 376
Publikováno v:
In Journal of Differential Equations 15 July 2020 269(3):1796-1828
Developing A.D. Aleksandrov's ideas, the first-named author of this article proposed the following approach to study of rigidity problems for the boundary of a $C^0$-submanifold in a smooth Riemannian manifold: Let $Y_1$ be a 2-dimensional compact co
Externí odkaz:
http://arxiv.org/abs/1401.7295