Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Tomasz Grzywny"'
Publikováno v:
Journal of Differential Equations. 340:273-308
We study heat kernels of Schrödinger operators whose kinetic terms are non-local operators built for sufficiently regular symmetric Lévy measures with radial decreasing profiles and potentials belong to Kato class. Our setting is fairly general and
Publikováno v:
Calculus of Variations and Partial Differential Equations. 62
We give Hardy-Stein and Douglas identities for nonlinear nonlocal Sobolev-Bregman integral forms with unimodal L\'evy measures. We prove that the corresponding Poisson integral defines an extension operator for the Sobolev-Bregman spaces. We also sho
Autor:
Karol Szczypkowski, Tomasz Grzywny
Publikováno v:
Forum Mathematicum. 33:1207-1236
We investigate densities of vaguely continuous convolution semigroups of probability measures on ℝ d {{\mathbb{R}^{d}}} . First, we provide results that give upper estimates in a situation when the corresponding jump measure is allowed to be highly
Autor:
Wojciech Cygan, Tomasz Grzywny
We introduce a notion of non-local perimeter which is defined through an arbitrary positive Borel measure on $${\mathbb {R}}^d$$ R d which integrates the function $$1\wedge |x|$$ 1 ∧ | x | . Such definition of non-local perimeter encompasses a wide
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::61408b1dc74e7ce6362a17de7c7f0ab8
http://arxiv.org/abs/2203.12343
http://arxiv.org/abs/2203.12343
Publikováno v:
Journal de Mathématiques Pures et Appliquées. 137:33-69
We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators. The extension is given by a suitable Poisson integral and solves the corresponding nonlocal Dirichlet problem. We give a Douglas-type formula for the quadratic
Autor:
Tomasz Grzywny, Karol Szczypkowski
Publikováno v:
Journal of Differential Equations. 267:6004-6064
Publikováno v:
Bulletin of the Malaysian Mathematical Sciences Society. 43:1223-1251
We prove that the Green function of the generator of symmetric unimodal Levy process with the weak lower scaling order bigger than one and the Green functions of its gradient perturbations are comparable for bounded \(C^{1,1}\) subsets of the real li
Publikováno v:
Mathematische Nachrichten. 292:805-825
In this paper we study the spectral heat content for various L\'evy processes. We establish the asymptotic behavior of the spectral heat content for L\'{e}vy processes of bounded variation in $\mathbb{R}^{d}$, $d\geq 1$. We also study the spectral he
Autor:
Karol Szczypkowski, Tomasz Grzywny
Publikováno v:
Bernoulli 26, no. 4 (2020), 3191-3223
We investigate densities of vaguely continuous convolution semigroups of probability measures on the Euclidean space. We expose that many typical conditions on the characteristic exponent repeatedly used in the literature of the subject are equivalen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c19554242ae1cb6058d478b3c5b8c826
https://projecteuclid.org/euclid.bj/1598493644
https://projecteuclid.org/euclid.bj/1598493644
Autor:
Mateusz Kwaśnicki, Tomasz Grzywny
Publikováno v:
Stochastic Processes and their Applications. 128:1-38
In the first part of this article, we prove two-sided estimates of hitting probabilities of balls, the potential kernel and the Green function for a ball for general isotropic unimodal L\'evy processes. Our bounds are sharp under the absence of the G