The “hot spots” conjecture for a certain class of planar convex domains

DOI10.1063/1.3251335zbMath1283.35016OpenAlexW2082394184WikidataQ123133599 ScholiaQ123133599MaRDI QIDQ3583669

Yasuhito Miyamoto

Publication date: 17 August 2010

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

Full work available at URL: https://doi.org/10.1063/1.3251335

zbMATH Keywords

boundary-value problemseigenvalues and eigenfunctions

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

The hot spots conjecture can be false: some numerical examples, A planar convex domain with many isolated ``hot spots on the boundary, An upper bound on the hot spots constant, Location of hot spots in thin curved strips, The ``hot spots conjecture for the Sierpiński gasket, Hot spots in convex domains are in the tips (up to an inradius), The ``hot spots conjecture on the Vicsek set, A spectral approach to the shortest path problem, On mixed Dirichlet-Neumann eigenvalues of triangles, Hot spots conjecture for a class of acute triangles

Cites Work

• The hot spots problem in planar domains with on hole
• Rearrangements and convexity of level sets in PDE
• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Instability results for reaction-diffusion equations with Neumann boundary conditions
• A counterexample to the ``hot spots conjecture
• On the ``hot spots conjecture of J. Rauch
• Nodal sets for ground states of Schrödinger operators with zero magnetic field in non simply connected domains
• On two conjectures in the fixed membrane eigenvalue problem
• An instability criterion for activator-inhibitor systems in a two-dimensional ball. II
• On the Zeros of Solutions to Ginzburg–Landau Type Systems
• Scaling coupling of reflecting Brownian motions and the hot spots problem
• On the structure of equilibrium phase transitions within the gradient theory of fluids
• On Neumann eigenfunctions in lip domains
• The “hot spots” conjecture for domains with two axes of symmetry
• On the shape of the stable patterns for activator-inhibitor systems in two-dimensional domains
• On the Local Behavior of Solutions of Non-Parabolic Partial Differential Equations