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Uniqueness in weighted Lebesgue spaces for an elliptic equation with drift on manifolds
Giulia Meglioli, Alberto Roncoroni
We investigate the uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of elliptic equations with a drift posed on a complete, noncompact, Riemannian manifold…
On the critical -Laplace equation
Giovanni Catino, Dario Daniele Monticelli, Alberto Roncoroni
In this paper we provide the classification of positive solutions to the critical Laplace equation on , for , possibly having infinite energy. If , or…
Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions
Giulio Ciraolo, Rosario Corso, Alberto Roncoroni
We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the t…
Serrin's type problems in warped product manifolds
Alberto Farina, Alberto Roncoroni
In this paper we consider Serrin's overdetermined problems in warped product manifolds and we prove Serrin's type rigidity results by using the P-function approach introduced by We…
Symmetry results for critical anisotropic -Laplacian equations in convex cones
Giulio Ciraolo, Alessio Figalli, Alberto Roncoroni
Given and , we consider the critical -Laplacian equation , which corresponds to critical points of the Sobolev inequality. Exploiting the…
The method of moving planes: a quantitative approach
Giulio Ciraolo, Alberto Roncoroni
We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's over…