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V. Burenkov, V. Gol’dshtein, A. Ukhlov (2014)
Conformal spectral stability estimates for the Dirichlet LaplacianMathematische Nachrichten, 288
L. Esposito, C. Nitsch, C. Trombetti (2011)
Best constants in Poincaré inequalities for convex domainsarXiv: Analysis of PDEs
P. Bassanini, A. Elcrat (1997)
Elliptic Partial Differential Equations of Second Order
J Zubelevich (2007)
An elliptic equation with perturbed $$p$$ p -Laplace operatorJ. Math. Anal. Appl., 328
D. Bertilsson (1999)
On Brennan's conjecture in conformal mapping
Daniele Valtorta (2011)
Sharp estimate on the first eigenvalue of the p-LaplacianNonlinear Analysis-theory Methods & Applications, 75
J. Heinonen, T. Kilpeläinen, O. Martio (1993)
Nonlinear Potential Theory of Degenerate Elliptic Equations
V. Burenkov, V. Gol'dshtein, A. Ukhlov (2014)
Conformal spectral stability for the Dirichlet-Laplace operatorarXiv: Spectral Theory
V. Gol'dshtein, A. Ukhlov (2016)
Spectral estimates of the $p$-Laplace Neumann operator in conformal regular domainsarXiv: Analysis of PDEs
V. Gol’dshtein, A. Ukhlov (2013)
Conformal Weights and Sobolev EmbeddingsJournal of Mathematical Sciences, 193
V. Ferone, C. Nitsch, C. Trombetti (2012)
A remark on optimal weighted Poincar\'e inequalities for convex domainsarXiv: Optimization and Control
SK Vodop’yanov, AD Ukhlov (2002)
Superposition operators in Sobolev spacesRuss. Math. (Izvestiya VUZ), 46
N. Kuznetsov, A. Nazarov (2015)
SHARP CONSTANTS IN THE POINCARÉ, STEKLOV AND RELATED INEQUALITIES (A SURVEY)Mathematika, 61
V. Gol'dshtein, A. Ukhlov (2014)
Brennan's Conjecture and universal Sobolev inequalitiesBulletin Des Sciences Mathematiques, 138
O. Zubelevich (2007)
An elliptic equation with perturbed p-Laplace operatorJournal of Mathematical Analysis and Applications, 328
P. Koskela, Jani Onninen, J. Tyson (2002)
Quasihyperbolic boundary conditions and Poincaré domainsMathematische Annalen, 323
S. Vodop’yanov, V. Gol'dshtein, Yu. Reshetnyak (1979)
ON GEOMETRIC PROPERTIES OF FUNCTIONS WITH GENERALIZED FIRST DERIVATIVESRussian Mathematical Surveys, 34
V. Gol'dshtein (1981)
Degree of summability of the generalized derivatives of quasic on formal homeomorphismsSiberian Mathematical Journal, 22
(2004)
Ukhlov, Set functions and their applications in the theory of Lebesgue and Sobolev spaces
G Pólya (1961)
On the eigenvalues of vibrating membranesProc. Lond. Math. Soc., 11
V. Gol'dshtein, A. Ukhlov (2007)
Weighted Sobolev spaces and embedding theoremsTransactions of the American Mathematical Society, 361
L. PAYlqE, H. Weinberger (1960)
An optimal Poincaré inequality for convex domainsArchive for Rational Mechanics and Analysis, 5
K Astala, P Koskela (1991)
Quasiconformal mappings and global integrability of the derivativeJ. Anal. Math., 57
K. Astala, T. Iwaniec, G. Martin (2009)
Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)
A. Beardon, D. Minda (2006)
The hyperbolic metric and geometric function theory
V. Gol'dshtein, A. Ukhlov (2012)
Brennan's conjecture for composition operators on Sobolev spacesarXiv: Complex Variables
P. Koskela, F. Reitich (1993)
Hölder continuity of Sobolev functions and quasiconformal mappingsMathematische Zeitschrift, 213
V Gol’dshtein, A Ukhlov (2016)
Spectral estimates of the $$p$$ p -Laplace Neumann operator in conformal regular domainsTrans. A. Razmadze Math. Inst., 170
S. Vodop’yanov, A. Ukhlov (2002)
Superposition operators in Sobolev spacesDoklady Mathematics, 66
S. Vodop’yanov, V. Gol'dshtein (1975)
Lattice isomorphisms of the spaces Wn1 and quasiconformal mappingsSiberian Mathematical Journal, 16
R Hurri-Syrjänen, SG Staples (1998)
A quasiconformal analogue of Brennan’s conjectureComplex Var. Theory Appl., 35
A Ukhlov (1993)
On mappings, which induce embeddings of Sobolev spacesSib. Math. J., 34
R. Hurri-Syrjänen, S. Staples (1998)
A quasiconformal analogue of brennan's conjectureComplex Variables and Elliptic Equations, 35
SK Vodop’yanov, AD Ukhlov (1998)
Sobolev spaces and $$(P, Q)$$ ( P , Q ) -quasiconformal mappings of Carnot groupsSib. Math. J., 39
V. Maz'ya (2011)
Sobolev Spaces: with Applications to Elliptic Partial Differential Equations
H. Hedenmalm, S. Shimorin (2004)
Weighted Bergman spaces and the integral means spectrum of conformal mappingsDuke Mathematical Journal, 127
K. Astala, P. Koskela (1991)
Quasiconformal mappings and global integrability of the derivativeJournal d’Analyse Mathématique, 57
B. Brandolini, F. Chiacchio, C. Trombetti (2009)
Sharp Estimates for Eigenfunctions of a Neumann ProblemCommunications in Partial Differential Equations, 34
S. Vodop’yanov, A. Ukhlov (1998)
Sobolev spaces and (P,Q)-quasiconformal mappings of carnot groupsSiberian Mathematical Journal, 39
J. Brennan (1978)
The Integrability of the Derivative in Conformal MappingJournal of The London Mathematical Society-second Series
G. Pólya (1961)
On the Eigenvalues of Vibrating Membranes(In Memoriam Hermann Weyl)Proceedings of The London Mathematical Society
P Koskela, J Onninen, JT Tyson (2002)
Quasihyperbolic boundary conditions and capacity: Poincaré domainsMath. Ann., 323
V. Gol’dshtein, A. Ukhlov (2015)
On the First Eigenvalues of Free Vibrating Membranes in Conformal Regular DomainsArchive for Rational Mechanics and Analysis, 221
B. Brandolini, F. Chiacchio, C. Trombetti (2013)
Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problemsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 145
V. Gol’dshtein, L. Gurov (1994)
Applications of change of variables operators for exact embedding theoremsIntegral Equations and Operator Theory, 19
SK Vodop’yanov, VM Gol’dstein (1975)
Lattice isomorphisms of the spaces $$W^1_n$$ W n 1 and quasiconformal mappingsSib. Math. J., 16
A. Ukhlov (1992)
On mappings generating the embeddings of Sobolev spacesSiberian Mathematical Journal, 34
K. Astala (1994)
Area distortion of quasiconformal mappingsActa Mathematica, 173
In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains $$\varOmega \subset {\mathbb {R}}^2$$ Ω ⊂ R 2 . This study is based on a quasiconformal version of the universal two-weight Poincaré–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal $$\alpha $$ α -regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings.
Bollettino dell Unione Matematica Italiana – Springer Journals
Published: May 17, 2017
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