5 papers
Stability of solutions of semilinear evolution equations with integro-differential operators
Andrzej Rozkosz, Leszek SÅomiÅski
We consider solutions of the Cauchy problem for semilinear equations with (possibly) different Lévy operators. We provide various results on their convergence under the assumption…
Nonlinear Hardy-Stein type identities for harmonic functions relative to symmetric integro-differential operators
Tomasz Klimsiak, Andrzej Rozkosz
We show identities of Hardy-Stein type for harmonic functions relative to integro-differential operators corresponding to general symmetric regular Dirichlet forms satisfying the a…
Robin problem with measure data and singular nonlinearities on the boundary
Andrzej Rozkosz
We consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving…
Reflected Skorokhod equations and the Neumann boundary value problem for elliptic equations with Levy-type operators
Andrzej Rozkosz, Leszek Slominski
We consider Neumann problem for linear elliptic equations involving integro-differential operators of Levy-type. We show that suitably defined viscosity solutions have probabilisti…
Dirichlet problem for semilinear partial integro-differential equations: the method of orthogonal projection
Tomasz Klimsiak, Andrzej Rozkosz
We study the Dirichlet problem for semilinear equations on general open sets with measure data on the right-hand side and irregular boundary data. For this purpose we develop the c…