Concavity principles for nonautonomous elliptic equations and applications

Article type: Research Article

Authors: Almousa, Nouf^a | Bucur, Claudia^b | Cornale, Roberta^c | Squassina, Marco^{d; c; *}

Affiliations: [a] Princess Nourah Bint Abdul Rahman University, PO Box 84428, Riyadh, Saudi Arabia | [b] Università degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy | [c] Università Cattolica del Sacro Cuore, Via della Garzetta 48, 25133, Brescia, Italy | [d] Princess Nourah Bint Abdul Rahman University, PO Box 84428, Riyadh, Saudi Arabia

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming to get almost concavity results for a relevant class of anisotropic semilinear elliptic problems with spatially dependent source and diffusion.

Keywords: Approximate convexity principles, anisotropic problems, semilinear elliptic problems

DOI: 10.3233/ASY-231863

Journal: Asymptotic Analysis, vol. 135, no. 3-4, pp. 509-524, 2023