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Regularity of solutions to a fractional elliptic problem with mixed Dirichlet-Neumann boundary data
(De Gruyter, 2021-10-01) Carmona, Jose; Colorado, Eduardo; Leonori, Tommaso; Ortega, Alejandro; 35996792500; 6507374993; 14521092300; 56489711800
In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the spectral fractional Laplacian.
A uniqueness result for a singular elliptic equation with gradient term
(Cambridge University Press, 2018-06-22) Carmona, José; Leonori, Tommaso; 35996792500; 14521092300
We prove the uniqueness of a solution for a problem whose simplest model is with k ≥ 1, 0 Lz(Ω) and Ω is a bounded domain of N, N ≥ 2. So far, uniqueness results are known for k < 1, while existence holds for any k ≥ 1 and f positive in open sets compactly embedded in a neighbourhood of the boundary. We extend the uniqueness results to the k ≥ 1 case and show, with an example, that existence does not hold if f is zero near the boundary. We even deal with the uniqueness result when f is replaced by a nonlinear term λuq with 0 < q < 1 and λ > 0.