Tomasz Klimsiak

activity

20092026

most citedDirichlet forms and semilinear elliptic equations with measure data

53 citations · 217 across the 49 of their papers we have counts for

collaborators

Showing 2018Show all

8 papers · 1 filter

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…

math.PR2018

BSDEs with monotone generator and two irregular reflecting barriers

Tomasz Klimsiak

We consider BSDEs with two reflecting irregular barriers. We give necessary and sufficient conditions for existence and uniqueness of $L^{p}$ solutions for equations with…

math.AP2018

Reflected BSDEs and obstacle problem for semilinear PDEs in divergence form

Tomasz Klimsiak

We consider the Cauchy problem for semilinear parabolic equation in divergence form with obstacle. We show that under natural conditions on the right-hand side of the equation and…

math.AP2018★ 2 cited

Smooth measures and capacities associated with nonlocal parabolic operators

Tomasz Klimsiak, Andrzej Rozkosz

We consider a family ${L_{t}, t \in [0, T]}$ of closed operators generated by a family of regular (non-symmetric) Dirichlet forms ${(B^{(t)}, V), t \in [0, T]}$ on $L^{2} (E; m)$ . We show…

math.AP2018

On the structure of diffuse measures for parabolic capacities

Tomasz Klimsiak, Andrzej Rozkosz

Let $Q = (0, T) \times Ω$ , where $Ω$ is a bounded open subset of $R^{d}$ . We consider the parabolic $p$ -capacity on $Q$ naturally associated with the usual $p$ -Laplacian. Droniou…

math.PR2018★ 1 cited

Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games

Tomasz Klimsiak

We introduce a new class of reflected backward stochastic differential equations with two càdlàg barriers, which need not satisfy any separation conditions. For that reason, in gen…

math.AP2018★ 3 cited

On semilinear elliptic equations with diffuse measures

Tomasz Klimsiak, Andrzej Rozkosz

We consider semilinear equation of the form $- Lu = f (x, u) + μ$ , where $L$ is the operator corresponding to a transient symmetric regular Dirichlet form $E$ , $μ$ is a diffuse…