Alberto Saldaña

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

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

s>0

Asymptotic axial symmetry of solutions of parabolic equations in bounded radial domains

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

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

s

Positive powers of the laplacian: From hypersingular integrals to boundary value problems

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

Qualitative properties of solutions to mixed-diffusion bistable equations

s

On the Asymptotic Shape of Solutions to Neumann Problems for Non-cooperative Parabolic Systems

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