We prove that quasi-concave positive solutions to a class of quasi-linear elliptic equations driven by the p-Laplacian in convex bounded domains of the plane have only one critical point. As a consequence, we obtain strict concavity results for suitable transformations of these solutions.
Borrelli, W., Mosconi, S., Squassina, M., Uniqueness of the critical point for solutions of some p-Laplace equations in the plane, <<ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI>>, 2023; 34 (1): 61-88. [doi:10.4171/RLM/997] [https://hdl.handle.net/10807/269615]
Uniqueness of the critical point for solutions of some p-Laplace equations in the plane
Borrelli, William;Squassina, Marco
2023
Abstract
We prove that quasi-concave positive solutions to a class of quasi-linear elliptic equations driven by the p-Laplacian in convex bounded domains of the plane have only one critical point. As a consequence, we obtain strict concavity results for suitable transformations of these solutions.
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