Sharp Estimates for Dirichlet Eigenfunctions in Simply Connected Domains

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 کامل

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 کامل

Harmonic 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 کامل

p 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 کامل

L1-Estimates for Eigenfunctions of the Dirichlet Laplacian

For d ∈ N and Ω 6= ∅ an open set in R, we consider the eigenfunctions Φ of the Dirichlet Laplacian −∆Ω of Ω. If Φ is associated with an eigenvalue below the essential spectrum of −∆Ω we provide estimates for the L1-norm of Φ in terms of its L2-norm and spectral data. These L1estimates are then used in the comparison of the heat content of Ω at time t > 0 and the heat trace at times t′ > 0, wher...

متن کامل

Sharp Estimates for Dirichlet Eigenfunctions in Simply Connected Domains

نویسندگان

چکیده

منابع مشابه

Hardy Inequalities for Simply Connected Planar Domains

Harmonic Measure in Simply Connected Domains

Harmonic Measure in Simply Connected Domains Revisited

p Harmonic Measure in Simply Connected Domains

L1-Estimates for Eigenfunctions of the Dirichlet Laplacian

ژورنال