Tomasz Klimsiak

activity

20162021

collaborators

12 papers

math.AP2021

Nonlinear elliptic equations with integro-differential divergence form operators and measure data under sign condition on the nonlinearity

Tomasz Klimsiak

We study existence problem for semilinear equations with Borel measure data and operator generated by a symmetric Markov semigroup. We assume merely that the nonlinear part satisfi…

math.AP2020

On the maximum principles and the quantitative version of the Hopf lemma for uniformly elliptic integro-differential operators

Tomasz Klimsiak, Tomasz Komorowski

In the present paper we prove estimates on {subsolutions of the equation $- A v + c (x) v = 0$ }, $x \in D$ , where $D \subset R^{d}$ is a domain (i.e. an open and connected set) and $A$ is a…

math.AP2020

On uniqueness and structure of renormalized solutions to integro-differential equations with general measure data

Tomasz Klimsiak

We propose a new definition of renormalized solution to linear equation with self-adjoint operator generating a Markov semigroup and bounded Borel measure on the right-hand side. W…

math.AP2019

Uniqueness for an obstacle problem arising from logistic-type equations with fractional Laplacian

Tomasz Klimsiak

We prove a uniqueness theorem for the obstacle problem for linear equations involving the fractional Laplacian with zero Dirichlet exterior condition. The problem under considerati…

math.PR2018

Reflected backward stochastic differential equations with two optional barriers

Tomasz Klimsiak, Maurycy Rzymowski, Leszek Słomiński

We consider reflected backward stochastic differential equations with two general optional barriers. The solutions to these equations have the so-called regulated trajectories, i.e…

math.PR2018

Reflected BSDEs with monotone generator

Tomasz Klimsiak

We give necessary and sufficient condition for existence and uniqueness of $L^{p}$ -solutions of reflected BSDEs with continuous barrier, generator monotone with respect to…