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math.AP2018
Local compactness and nonvanishing for weakly singular nonlocal quadratic forms
Sven Jarohs, Tobias Weth
In this work we study a class of nonlocal quadratic forms given by \[ \mathcal{E}_j(u,v)=\frac{1}{2}\int_{\mathbb{R}^N}\int_{\mathbb{R}^N}(u(x)-u(y))(v(x)-v(y))j(x-y)\ dxdy, \] whe…
math.AP2018
Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions
Nicola Abatangelo, Serena Dipierro, Mouhamed Moustapha Fall +2
We present explicit formulas for solutions to nonhomogeneous boundary value problems involving any positive power of the Laplacian in the half-space. For non-integer powers the ope…