Dipierro, S.Gonçalves da Silva, J.Poggesi, G.Valdinoci, E.2025-10-232025-10-232025Journal of Functional Analysis, 2025; 289(10):111108-1-111108-380022-12361096-0783https://hdl.handle.net/2440/147956We prove a quantitative version of a Gidas-Ni-Nirenberg-type symmetry result involving the p-Laplacian. Quantitative stability is achieved here via integral identities based on the proof of rigidity established by J. Serra in 2013, which extended to general dimension and the p-Laplacian operator an argument proposed by P.-L. Lions in dimension 2for the classical Laplacian. Stability results for the classical Gidas-Ni-Nirenberg sym- metry theorem (involving the classical Laplacian) via the method of moving planes were established by Rosset in 1994 and by Ciraolo, Cozzi, Perugini, Pollastro in 2024. To the authors’ knowledge, the present paper provides the fifirst quantitative Gidas-Ni-Nirenberg-type result involving the p Laplacian for p ≠ 2. Even for the classical Laplacian (i.e., for p=2), this is the fifirst time that integral identities are used to achieve stability for a Gidas-Ni-Nirenberg-type result.en© 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.Gidas-Ni-Nirenberg Theorem; p-Laplacian; Approximate symmetry; Quantitative stabilityJournal article10.1016/j.jfa.2025.111108744256Poggesi, G. [0000-0002-3961-542X]