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math.AP2023★ 6 cited
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…
math.AP2023
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…