# Serrin’s type overdetermined problems in convex cones

@article{Ciraolo2018SerrinsTO, title={Serrin’s type overdetermined problems in convex cones}, author={Giulio Ciraolo and Alberto Roncoroni}, journal={Calculus of Variations and Partial Differential Equations}, year={2018}, volume={59}, pages={1-21} }

We consider overdetermined problems of Serrin’s type in convex cones for (possibly) degenerate operators in the Euclidean space as well as for a suitable generalization to space forms. We prove rigidity results by showing that the existence of a solution implies that the domain is a spherical sector.

#### 9 Citations

An exterior overdetermined problem for Finsler $N$-laplacian in convex cones

- Mathematics
- 2021

We consider a partially overdetermined problem for anisotropic N-Laplace equations in a convex cone Σ intersected with the exterior of a bounded domain Ω in R , N ≥ 2. Under a prescribed logarithmic… Expand

Radial symmetry and partially overdetermined problems in a convex cone

- Mathematics
- 2020

We obtain the radial symmetry of the solution to a partially overdetermined boundary value problem in a convex cone in space forms by using the maximum principle for a suitable subharmonic function… Expand

Serrin’s type problems in warped product manifolds

- Mathematics
- 2019

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 Weinberger.

Isoperimetric cones and minimal solutions of partial overdetermined problems

- Mathematics
- 2019

In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which… Expand

A partially overdetermined problem in a half ball

- Mathematics, Physics
- Calculus of Variations and Partial Differential Equations
- 2019

In this paper, we study a partially overdetermined mixed boundary value problem in a half ball. We prove that a domain in which this partially overdetermined problem admits a solution if and only if… Expand

An overdetermined problem associated to the Finsler Laplacian

- Mathematics
- 2020

We prove a rigidity result for the anisotropic Laplacian. More precisely, the domain of the problem is bounded by an unknown surface supporting a Dirichlet condition together with a Neumann-type… Expand

Symmetry results for critical anisotropic p-Laplacian equations in convex cones

- Mathematics
- 2019

Given $n \geq 2$ and $1<p<n$, we consider the critical $p$-Laplacian equation $\Delta_p u + u^{p^*-1}=0$, which corresponds to critical points of the Sobolev inequality. Exploiting the moving planes… Expand

Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities

- Mathematics
- 2021

For 1 < p < ∞, we prove radial symmetry for bounded nonnegative solutions of

A partially overdetermined problem in domains with partial umbilical boundary in space forms

- Mathematics
- 2020

In this paper, we consider a partially overdetermined mixed boundary value problem in space forms. We generalize the main result in \cite{GX} into the case of general domains with partial umbilical… Expand

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