53 citations · 217 across the 49 of their papers we have counts for
10 papers · 1 filter
Semilinear elliptic equations with Dirichlet operator and singular nonlinearities
Tomasz Klimsiak
In the paper we consider elliptic equations of the form , where is the operator associated with a regular symmetric Dirichlet form, is a positive nontrivi…
Reduced measures for semilinear elliptic equations involving Dirichlet operators
Tomasz Klimsiak
We consider elliptic equations of the form (E) , where is a negative definite self-adjoint Dirichlet operator, is a function which is continuous and nonincrea…
Obstacle problem for evolution equations involving measure data and operator corresponding to semi-Dirichlet form
Tomasz Klimsiak
In the paper, we consider the obstacle problem, with one and two irregular barriers, for semilinear evolution equation involving measure data and operator corresponding to a semi-D…
Systems of quasi-variational inequalities related to the switching problem
Tomasz Klimsiak
We prove the existence of weak solution for a system of quasi-variational inequalities related to a switching problem with dynamic driven by operator associated with a semi-Dirichl…
Renormalized solutions of semilinear elliptic equations with general measure data
Tomasz Klimsiak, Andrzej Rozkosz
In the paper, we first propose a definition of renormalized solution of semilinear elliptic equation involving operator corresponding to a general (possibly nonlocal) symmetric reg…
Reflected BSDEs with regulated trajectories
Tomasz Klimsiak, Maurycy Rzymowski, Leszek Słomiński
We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e trajectories with left and right finite limits. We pro…
Systems of semilinear parabolic variational inequalities with time-dependent convex obstacles
Tomasz Klimsiak, Andrzej Rozkosz, Leszek Slominski
We consider a system of seminlinear parabolic variational inequalities with time-dependent convex obstacles. We prove the existence and uniqueness of its solution. We also provide…
Nonlinear parabolic SPDEs involving Dirichlet operators
Tomasz Klimsiak, Andrzej Rozkosz
We study the problem of existence, uniqueness and regularity of probabilistic solutions of the Cauchy problem for nonlinear stochastic partial differential equations involving oper…
Large time behaviour of solutions to parabolic equations with Dirichlet operators and nonlinear dependence on measure data
Tomasz Klimsiak, Andrzej Rozkosz
We study large time behaviour of solutions of the Cauchy problem for equations of the form , where is the operator associated with a reg…
The valuation of American options in a multidimensional exponential Levy model
Tomasz Klimsiak, Andrzej Rozkosz
We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully exam…