Fiber Brownian motion and the ``hot spots problem

DOI10.1215/S0012-7094-00-10512-1zbMath1006.60078MaRDI QIDQ1847771

Krzysztof Burdzy, Richard F. Bass

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

coupling methodreflected Brownian motionfiber Brownian motionsecond Neumann eigenfunction

Mathematics Subject Classification ID

Brownian motion (60J65) Spectral theory and eigenvalue problems for partial differential equations (35P99) Diffusion processes (60J60) Probabilistic potential theory (60J45) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

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Pinching and twisting Markov processes, The hot spots conjecture can be false: some numerical examples, Efficient Markovian couplings: Examples and counterexamples., Simultaneous boundary hitting by coupled reflected Brownian motions, The hot spots conjecture on a class of domains in \(\mathbb R^n\) with \( n \geqslant 3\), A planar convex domain with many isolated ``hot spots on the boundary, Improved upper bounds for the hot spots constant of Lipschitz domains, An upper bound on the hot spots constant, On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems, Location of hot spots in thin curved strips, Hot spots in convex domains are in the tips (up to an inradius), Stochastic averaging with a flattened Hamiltonian: A Markov process on a stratified space (a whiskered sphere), Brownian motion with killing and reflection and the ``hot-spots problem, A spectral approach to the shortest path problem, Neumann Bessel heat kernel monotonicity, On Neumann eigenfunctions in lip domains, Comparison of potential theoretic properties of rough domains, Traps for reflected Brownian motion, The “hot spots” conjecture for domains with two axes of symmetry, Efficient Markovian couplings: Examples and counterexamples, The hot spots problem in planar domains with on hole, Scaling coupling of reflecting Brownian motions and the hot spots problem

Cites Work

• The construction of Brownian motion on the Sierpinski carpet
• Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains
• Efficient Markovian couplings: Examples and counterexamples
• Rearrangements and convexity of level sets in PDE
• A counterexample to the ``hot spots conjecture
• On the ``hot spots conjecture of J. Rauch
• Diffusion processes and their sample paths.
• The “hot spots” conjecture for domains with two axes of symmetry
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