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math.AP2025
Fractional critical systems with mixed boundary conditions
R. Kumar, A. Ortega
In this paper, we analyze the existence of solution for a fractional elliptic system coupled by critical nonlinearities and endowed with mixed Dirichlet-Neumann boundary conditions…
math.AP2025
Nonlocal critical problems with mixed boundary conditions and nearly resonant perturbations
Eduardo Colorado, Giovanni Monica Bisci, Alejandro Ortega +1
We consider the following nonlocal critical problem with mixed Dirichlet-Neumann boundary conditions, \begin{equation} \left\{ \begin{array}{ll} (-Î)^su=λu+|u|^{2_s^*-2}u &\text{…
math.AP2025
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 $…