Spectral estimates of the p-Laplace Neumann operator in conformal regular domains
In this paper we study spectral estimates of the p-Laplace Neumann operator in conformal regular domains Ω⊂R2. This study is based on (weighted) Poincaré–Sobolev inequalities. The main technical tool is the theory of composition operators in relation with the Brennan’s conjecture. We prove that if t...
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2016-05-01
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| Series: | Transactions of A. Razmadze Mathematical Institute |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2346809216000167 |
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doaj-79cbc3282a2c422c836f589ff35286562020-11-24T22:49:52ZengElsevierTransactions of A. Razmadze Mathematical Institute2346-80922016-05-011701137148Spectral estimates of the p-Laplace Neumann operator in conformal regular domainsV. Gol’dshtein0A. Ukhlov1Corresponding author. Tel.: +972 86461620; fax: +972 86477648.; Department of Mathematics, Ben-Gurion University of the Negev, P. O. Box 653, Beer Sheva, 84105, IsraelDepartment of Mathematics, Ben-Gurion University of the Negev, P. O. Box 653, Beer Sheva, 84105, IsraelIn this paper we study spectral estimates of the p-Laplace Neumann operator in conformal regular domains Ω⊂R2. This study is based on (weighted) Poincaré–Sobolev inequalities. The main technical tool is the theory of composition operators in relation with the Brennan’s conjecture. We prove that if the Brennan’s conjecture holds for any p∈(4/3,2) and r∈(1,p/(2−p)) then the weighted (r,p)-Poincare–Sobolev inequality holds with the constant depending on the conformal geometry of Ω. As a consequence we obtain classical Poincare–Sobolev inequalities and spectral estimates for the first nontrivial eigenvalue of the p-Laplace Neumann operator for conformal regular domains. Keywords: Conformal mappings, Sobolev spaces, Elliptic equationshttp://www.sciencedirect.com/science/article/pii/S2346809216000167 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
V. Gol’dshtein A. Ukhlov |
| spellingShingle |
V. Gol’dshtein A. Ukhlov Spectral estimates of the p-Laplace Neumann operator in conformal regular domains Transactions of A. Razmadze Mathematical Institute |
| author_facet |
V. Gol’dshtein A. Ukhlov |
| author_sort |
V. Gol’dshtein |
| title |
Spectral estimates of the p-Laplace Neumann operator in conformal regular domains |
| title_short |
Spectral estimates of the p-Laplace Neumann operator in conformal regular domains |
| title_full |
Spectral estimates of the p-Laplace Neumann operator in conformal regular domains |
| title_fullStr |
Spectral estimates of the p-Laplace Neumann operator in conformal regular domains |
| title_full_unstemmed |
Spectral estimates of the p-Laplace Neumann operator in conformal regular domains |
| title_sort |
spectral estimates of the p-laplace neumann operator in conformal regular domains |
| publisher |
Elsevier |
| series |
Transactions of A. Razmadze Mathematical Institute |
| issn |
2346-8092 |
| publishDate |
2016-05-01 |
| description |
In this paper we study spectral estimates of the p-Laplace Neumann operator in conformal regular domains Ω⊂R2. This study is based on (weighted) Poincaré–Sobolev inequalities. The main technical tool is the theory of composition operators in relation with the Brennan’s conjecture. We prove that if the Brennan’s conjecture holds for any p∈(4/3,2) and r∈(1,p/(2−p)) then the weighted (r,p)-Poincare–Sobolev inequality holds with the constant depending on the conformal geometry of Ω. As a consequence we obtain classical Poincare–Sobolev inequalities and spectral estimates for the first nontrivial eigenvalue of the p-Laplace Neumann operator for conformal regular domains. Keywords: Conformal mappings, Sobolev spaces, Elliptic equations |
| url |
http://www.sciencedirect.com/science/article/pii/S2346809216000167 |
| work_keys_str_mv |
AT vgoldshtein spectralestimatesoftheplaplaceneumannoperatorinconformalregulardomains AT aukhlov spectralestimatesoftheplaplaceneumannoperatorinconformalregulardomains |
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1725674771632357376 |