Comparison results for a nonlocal singular elliptic problem

Article type: Research Article

Authors: Brandolini, Barbara^a | de Bonis, Ida^b | Ferone, Vincenzo^{c; *} | Volzone, Bruno^d

Affiliations: [a] Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, via Archirafi 34, 90123 Palermo, Italy | [b] Dipartimento di Pianificazione, Design, Tecnologia dell’Architettura, Sapienza Università di Roma, via Flaminia 72, 00196 Roma, Italy | [c] Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, Complesso Univ. Monte S. Angelo, via Cintia, 80126 Napoli, Italy | [d] Dipartimento di Scienze Economiche, Giuridiche, Informatiche e Motorie, Università degli Studi di Napoli “Parthenope”, Centro direzionale, Isola C4, 80143 Napoli, Italy

Correspondence: [*] Corresponding author. E-mail: ferone@unina.it.

Abstract: We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are presented, depending on the summability of the right-hand side of the equation. The maximum principle arguments employed in the core of the proofs of the main results offer a nonstandard, flexible alternative to the ones described in (Arch. Ration. Mech. Anal. 239 (2021) 1733–1770, Theorem 31). Some interesting consequences are Lp regularity results and nonlocal energy estimates for solutions.

Keywords: Symmetrization, fractional Laplacian, nonlocal elliptic equations, singular elliptic equations

DOI: 10.3233/ASY-231860

Journal: Asymptotic Analysis, vol. 135, no. 3-4, pp. 421-444, 2023