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math.AP2017
Positive powers of the Laplacian: from hypersingular integrals to boundary value problems
Nicola Abatangelo, Sven Jarohs, Alberto Saldaña
Any positive power of the Laplacian is related via its Fourier symbol to a hypersingular integral with finite differences. We show how this yields a pointwise evaluation which is m…
math.AP2017
Integral representation of solutions to higher-order fractional Dirichlet problems on balls
Nicola Abatangelo, Sven Jarohs, Alberto Saldaña
We provide closed formulas for (unique) solutions of nonhomogeneous Dirichlet problems on balls involving any positive power of the Laplacian. We are able to prescribe values…
math.AP2017
Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions
Alberto Saldaña, Hugo Tavares
We study existence, regularity, and qualitative properties of solutions to the system \[ -Δu = |v|^{q-1} v\quad \text{ in }Ω,\qquad -Δv = |u|^{p-1} u\quad \text{ in }Ω,\qquad \part…