Sven Jarohs

Integral representation of solutions to higher-order fractional Dirichlet problems on balls

We provide closed formulas for (unique) solutions of nonhomogeneous Dirichlet problems on balls involving any positive power

Symmetry of solutions to nonlocal nonlinear boundary value problems in radial sets

s>0

Strong Comparison Principle for the Fractional p-Laplacian and Applications to Starshaped Rings

of the Laplacian. We are able to prescribe values outside the domain and boundary data of different orders using explicit Poisson-type kernels and a new notion of higher-order boundary operator, which recovers normal derivatives if

Symmetry via antisymmetric maximum principles in nonlocal problems of variable order

s

Overdetermined problems with fractional laplacian

is a natural number. Our results unify and generalize previous approaches in the study of polyharmonic operators and fractional Laplacians. As applications, we show a novel characterization of

Asymptotic symmetry for a class of nonlinear fractional reaction-diffusion equations

s

Green function and Martin kernel for higher-order fractional Laplacians in balls

-harmonic functions in terms of Martin kernels, a higher-order fractional Hopf Lemma, and examples of positive and sign-changing Green functions.

On the loss of maximum principles for higher-order fractional Laplacians

AbstractFor open radial sets

Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions

{\Omega \subset {\mathbb {R}}^N}