Special Session 65: Geometry of PDEs on Manifolds and Nilpotent Lie Groups

Varadhan-type asymptotics for boundary data with localized support
Diego Berti
Univeristy of Turin
Italy
Co-Author(s):    
Abstract:
We study short-time and small-diffusion asymptotics for linear, uniformly elliptic operators with variable coefficients in a bounded domain. For nonconstant boundary data, we show that the leading behavior is governed by the intrinsic distance, induced by the operator, to the support of the boundary datum. This extends the classical Varadhan result, originally obtained for constant boundary data, and emphasizes the role of the localized source. This is joint work with Michele Marini (University del Sannio, Italy) and Rolando Magnanini (University di Firenze, Italy).