From the 1 of 7 linked papers with an AI index.
7 papers
Isolated Singularities and Measure Data Problems for Semilinear Equations Driven by Stable Lévy Operators
Kamil Dunst, Tomasz Klimsiak
The paper studies positive solutions of semilinear equations driven by uniformly elliptic stable Lévy operators, showing that isolated singularities correspond to Dirac masses and…
Existence of Positive Solutions to Semilinear Equations with Sublinear Nonlinearities and Compact Positivity-Improving Resolvent
Tomasz Klimsiak
We prove a Brézis--Oswald type existence theorem for positive solutions of semilinear equations in an abstract setting in which the underlying linear operator has a compact positi…
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…
Bôcher type theorem for elliptic equations with drift perturbed Lévy operator
Tomasz Klimsiak
A classical Bôcher's theorem asserts that any positive harmonic function (with respect to the Laplacian) in the punctured unit ball can be expressed, up to the multiplication cons…
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…
Homogenization of stable-like operators with random, ergodic coefficients
Tomasz Klimsiak, Tomasz Komorowski, Lorenzo Marino
We show homogenization for a family of -valued stable-like processes , , whose (random) Fourier symbols equal $q_ε(x,ξ;θ)=\frac…