Short—time Asymptotics of the Heat Kernel of the Laplacian for a Multiply-connected Domain in R² with Robin Boundary Conditions

Abstract

The trace of the heat kernel are the eigenvalues of the negative Laplacian plane, is studied for a multiply—connected bounded domain Ω in R ² surrounding by simply connected bounded domains fy with smooth boundaries where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth parts of the boundaries is considered, where and Some applications of θ (t) for an ideal gas enclosed in the multiply—connected bounded container Ω with Robin boundary conditions are given.

Keywords:

• Inverse problem
• the trace of the heat kernel
• Schrödinger equation
• classical ideal gas

AMS:

• 35K99
• 35P05
• 35P99