187 citations · 856 across the 36 of their papers we have counts for
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Free Boundary Problems: The Forefront of Current and Future Developments
Gui-Qiang Chen, Henrik Shahgholian, Juan-Luis Vazquez
This is an introduction to The Theme Issue on "Free Boundary Problems and Related Topics", which consists of 14 survey/review articles on the topics, of Philosophical Transactions…
Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application
Yannick Sire, Juan Luis Vazquez, Bruno Volzone
We develop further the theory of symmetrization of fractional Laplacian operators contained in recent works of two of the authors. The theory leads to optimal estimates in the form…
Existence of maximal solutions for some very singular nonlinear fractional diffusion equations in 1D
Juan Luis Vazquez
We consider nonlinear parabolic equations involving fractional diffusion of the form with , and solve an open problem concerning the existen…
Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations
Matteo Bonforte, Antonio Segatti, Juan Luis Vazquez
We show non-existence of solutions of the Cauchy problem in for the nonlinear parabolic equation involving fractional diffusion with…
Some Free Boundary Problems involving Nonlocal Diffusion and Aggregation
Jose Antonio Carrillo, Juan Luis Vazquez
We report on recent progress in the study of evolution processes involving degenerate parabolic equations what may exhibit free boundaries. The equations we have selected follow to…