Title: | On qualitative properties of solutions for elliptic problems with the p-Laplacian through domain perturbations |
Authors: | Bobkov, Vladimír Kolonitskii, Sergey |
Citation: | BOBKOV, V. ., KOLONITSKII, S. . On qualitative properties of solutions for elliptic problems with the p-Laplacian through domain perturbations. Communications in partial differential equations, 2020, roč. 45, č. 3, s. 230-252. ISSN 0360-5302. |
Issue Date: | 2020 |
Publisher: | Taylor & Francis |
Document type: | článek article |
URI: | 2-s2.0-85074414532 http://hdl.handle.net/11025/36953 |
ISSN: | 0360-5302 |
Keywords in different language: | p-Laplacian;superlinear nonlinearity;domain derivative;shape optimization;Hadamard formula;Nehari manifold;least energy solution;nodal solution;nonradiality. |
Abstract: | We study the dependence of least nontrivial critical levels of the energy functional corresponding to the zero Dirichlet problem −Δ_p u=f(u) in a bounded domain Ω⊂R^N upon domain perturbations. Assuming that the nonlinearity f is superlinear and subcritical, we establish Hadamard-type formulas for such critical levels. As an application, we show that among all (generally eccentric) spherical annuli Ω least nontrivial critical levels attain maximum if and only if Ω is concentric. As a consequence of this fact, we prove the nonradiality of least energy nodal solutions whenever Ω is a ball or concentric annulus. |
Rights: | Plný text není přístupný. © Taylor & Francis |
Appears in Collections: | Články / Articles (NTIS) OBD |
Files in This Item:
File | Size | Format | |
---|---|---|---|
Bobkov_Kolonitskii-Published-2020.pdf | 2,11 MB | Adobe PDF | View/Open Request a copy |
Please use this identifier to cite or link to this item:
http://hdl.handle.net/11025/36953
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.