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math.AP2024
Positive solutions for a weighted critical problem with mixed boundary conditions
Alejandro Ortega, Luca Vilasi, Youjun Wang
We analyze the existence and multiplicity of positive solutions to a nonlocal elliptic problem involving the spectral fractional Laplace operator endowed with homogeneous mixed Dir…
math.AP2024
New functional inequalities with applications to the arctan-fast diffusion equation
Rafael Granero-Belinchón, Martina Magliocca, Alejandro Ortega
In this paper, we prove a couple of new nonlinear functional inequalities of Sobolev type akin to the logarithmic Sobolev inequality. In particular, one of the inequalities reads $…