A priori estimates and application to the symmetry of solutions for critical $p$-Laplace equations
By J. Vétois. 2014
121 citations recorded by the source corpus.
We establish pointwise a priori estimates for solutions in $D^{1,p}(\mathbb{R}^n)$ of equations of type $-\Delta_pu=f(x,u)$, where $p\in(1,n)$, $\Delta_p:=\mbox{div}\big(\left|\nabla u\right|^{p-2}\nabla u\big)$ is the $p$-Laplace operator, and $f$ is a Caratheodory function with critical Sobolev growth. In the case of positive solutions, our estimates allow us to extend previous radial symmetry results. In particular, by combining our results and a result of Damascelli-Ramaswamy, we are able to extend a recent result of Damascelli-Merch\'an-Montoro-Sciunzi on the symmetry of positive solutions in $D^{1,p}(\mathbb{R}^n)$ of the equation $-\Delta_pu=u^{p^*-1}$, where $p^*:=np/(n-p)$.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/3d6d96724d838719869639505893f2f70efd3c66
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In Applied Mathematics
- Alessio Figalli
- Giulio Ciraolo
- D. Monticelli
- A. Roncoroni
- G. Catino
- Guido De Philippis
- Max Fathi
- Dario Trevisan
In Computational Theory and Mathematics
- Giulio Ciraolo
- A. Roncoroni
- Alessio Figalli
- D. Monticelli
- G. Catino
- N. Fusco
- G. Peyr'e
- Adrien Blanchet
Citations in the corpus
- On the critical p-Laplace equation (2022, methodology): “Nevertheless the method of moving planes has been exploited in [9, 25, 31] to prove the following classification result: Let u be a positive weak solution of equation (1.”
- Symmetry results for critical anisotropic p-Laplacian equations in convex cones (2019, background): “Recently, in [45] and [37], positive solutions to (1.”