10 citations · 25 across the 7 of their papers we have counts for
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Optimal regularity of stable solutions to nonlinear equations involving the -Laplacian
Xavier Cabre, Pietro Miraglio, Manel Sanchon
We consider the equation in a smooth bounded domain of , where is the -Laplace operator. Explicit examples of unbounded stable energy solution…
(Non)local -convergence
Serena Dipierro, Pietro Miraglio, Enrico Valdinoci
We present some long-range interaction models for phase coexistence which have recently appeared in the literature, recalling also their relation to classical interface and capilla…
Universal Hardy-Sobolev inequalities on hypersurfaces of Euclidean space
Xavier Cabre, Pietro Miraglio
In this paper we study Hardy-Sobolev inequalities on hypersurfaces of , all of them involving a mean curvature term and having universal constants independent of…
Energy asymptotics of a Dirichlet to Neumann problem related to water waves
Pietro Miraglio, Enrico Valdinoci
We consider a Dirichlet to Neumann operator arising in a model for water waves, with a nonlocal parameter . We deduce the expression of the operator in…
Boundedness of stable solutions to nonlinear equations involving the -Laplacian
Pietro Miraglio
We consider stable solutions to the equation in a smooth bounded domain for a nonlinearity . Either in the radial case, or for s…
Symmetry results for the solutions of a partial differential equation arising in water waves
Serena Dipierro, Pietro Miraglio, Enrico Valdinoci
This paper recalls some classical motivations in fluid dynamics leading to a partial differential equation which is prescribed on a domain whose boundary possesses two connected co…
One-dimensional symmetry for the solutions of a three-dimensional water wave problem
Eleonora Cinti, Pietro Miraglio, Enrico Valdinoci
We prove a one-dimensional symmetry result for a weighted Dirichlet-to-Neumann problem arising in a model for water waves in dimension 3. More precisely we prove that minimizers an…