Abstract
We consider positive singular solutions (i.e. with a non-removable singularity) of a system of PDEs driven by p-Laplacian operators and with the additional presence of a nonlinear first order term. By a careful use of a rather new version of the moving plane method, we prove the symmetry of the solutions. The result is already new in the scalar case.
Funding source: Ministero dell’Università e della Ricerca
Award Identifier / Grant number: 2017JPCAPN
Funding source: Agencia Estatal de Investigación
Award Identifier / Grant number: PDI2019-110712GB-100
Funding statement: The authors are members of INdAM. F. Esposito and L. Montoro are partially supported by PRIN project 2017JPCAPN (Italy): Qualitative and quantitative aspects of nonlinear PDEs. L. Montoro is partially supported by Agencia Estatal de Investigación (Spain): project PDI2019-110712GB-100.
Acknowledgements
We would like to thank the anonymous referee for the careful reading of our manuscript.
References
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Articles in the same Issue
- Frontmatter
- Another proof of the existence of homothetic solitons of the inverse mean curvature flow
- A Weierstrass extremal field theory for the fractional Laplacian
- Minimizing movements for anisotropic and inhomogeneous mean curvature flows
- A singular Yamabe problem on manifolds with solid cones
- Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball
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