Eigenfunctions of the Koch snowflake domain

DOI10.1007/BF02099432zbMath0857.35093OpenAlexW2140413564MaRDI QIDQ1908061

M. M. H. Pang, Michel L. Lapidus

Publication date: 9 March 1997

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02099432

zbMATH Keywords

fractal boundariesestimates for the Dirichlet eigenfunction

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (17)

SPECTRUM AND HEAT KERNEL ASYMPTOTICS ON GENERAL LAAKSO SPACES ⋮ Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary ⋮ Fractal snowflake domain diffusion with boundary and interior drifts ⋮ LOCALIZATION ON SNOWFLAKE DOMAINS ⋮ 3D Koch-type crystals ⋮ Eigenfrequencies of fractal drums ⋮ Quasi-linear variable exponent boundary value problems with Wentzell-Robin and Wentzell boundary conditions ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Computing eigenfunctions on the Koch snowflake: a new grid and symmetry. ⋮ Computation of sharp estimates of the Poincaré constant on planar domains with piecewise self-similar boundary ⋮ Fractal tiles and quasidisks ⋮ The Sound of Fractal Strings and the Riemann Hypothesis ⋮ Hardy inequality and weighted heat trace ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back ⋮ Spectroscopy of drums and quantum billiards: Perturbative and nonperturbative results ⋮ Spectral Properties of Laplacians on Snowflake Domains and Filled Julia Sets ⋮ Lower bound gradient estimates for solutions of schrodinger equations and heat kernels

Cites Work

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• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Intrinsic ultracontractivity and eigenfunction estimates for Schrödinger operators
• Estimates for Conformal Maps of Strip Domains without Boundary Regularity
• On Strong Barriers and an Inequality of Hardy for Domains in R ⁿ

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