Ratio inequalities for heat kernels

Majid Hosseini, Purdue University

Abstract

Let U be a domain, convex in x and symmetric about the y axis, which is contained in a centered and oriented rectangle S. We prove Qt( U+)/Qt(U) ≤ Qt(S+)/Q t(S) where Qt stands for heat content, i.e. the remaining heat in the domain at time t if it initially has uniform temperature 1, with Dirichlet boundary conditions, where A+ = A ∩ {(x, y) : x > 0}. We also show that the analog of this inequality holds for some other Schrödinger operators.

Degree

Ph.D.

Advisors

Davis, Purdue University.

Subject Area

Mathematics

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