Szegö-Weinberger type inequalities for symmetric domains in simply connected space forms
نویسندگان
چکیده
We consider the Neumann eigenvalue problem for Laplacian on a bounded multi-connected domain contained in simply connected space forms. Under certain symmetry assumptions domain, we prove Szegö-Weinberger type inequalities first n positive eigenvalues.
منابع مشابه
Hardy Inequalities for Simply Connected Planar Domains
In 1986 A. Ancona showed, using the Koebe one-quarter Theorem, that for a simply-connected planar domain the constant in the Hardy inequality with the distance to the boundary is greater than or equal to 1/16. In this paper we consider classes of domains for which there is a stronger version of the Koebe Theorem. This implies better estimates for the constant appearing in the Hardy inequality. ...
متن کاملHarmonic Measure in Simply Connected Domains
Let Ω be a bounded simply connected domain in the complex plane, C. Let N be a neighborhood of ∂Ω, let p be fixed, 1 < p < ∞, and let û be a positive weak solution to the p Laplace equation in Ω ∩N. Assume that û has zero boundary values on ∂Ω in the Sobolev sense and extend û to N \ Ω by putting û ≡ 0 on N \ Ω. Then there exists a positive finite Borel measure μ̂ on C with support contained in ...
متن کاملHarmonic Measure in Simply Connected Domains Revisited
Let Ω be a bounded simply connected domain in the complex plane, C. Let N be a neighborhood of ∂Ω, let p be fixed, 1 < p < ∞, and let û be a positive weak solution to the p Laplace equation in Ω ∩N. Assume that û has zero boundary values on ∂Ω in the Sobolev sense and extend û to N \ Ω by putting û ≡ 0 on N \ Ω. Then there exists a positive finite Borel measure μ̂ on C with support contained in ...
متن کاملp Harmonic Measure in Simply Connected Domains
Let Ω be a bounded simply connected domain in the complex plane, C. Let N be a neighborhood of ∂Ω, let p be fixed, 1 < p < ∞, and let û be a positive weak solution to the p Laplace equation in Ω ∩N. Assume that û has zero boundary values on ∂Ω in the Sobolev sense and extend û to N \ Ω by putting û ≡ 0 on N \ Ω. Then there exists a positive finite Borel measure μ̂ on C with support contained in ...
متن کاملTree-like Decompositions of Simply Connected Domains
We show that any simply connected rectifiable domain Ω can be decomposed into Lipschitz crescents using only crosscuts of the domain and using total length bounded by a multiple of the length of ∂Ω. In particular, this gives a new proof of a theorem of Peter Jones that such a domain can be decomposed into Lipschitz disks. 1991 Mathematics Subject Classification. Primary: 68U05 Secondary: 26B15,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2022
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2022.126429