On the Schrödinger heat kernel in horn-shaped domains

• Autorzy: Gabriele Grillo
• Języki publikacji: EN

Abstrakty

EN

We prove pointwise lower bounds for the heat kernel of Schrödinger semigroups on Euclidean domains under Dirichlet boundary conditions. The bounds take into account non-Gaussian corrections for the kernel due to the geometry of the domain. The results are applied to prove a general lower bound for the Schrödinger heat kernel in horn-shaped domains without assuming intrinsic ultracontractivity for the free heat semigroup.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 35B05: Oscillation, zeros of solutions, mean value theorems, etc.
• 58J35: Heat and other parabolic equation methods
• 35B40: Asymptotic behavior of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 99
• Numer: 2
• Strony: 145-155

Daty

wydano

2004

Twórcy

autor

Gabriele Grillo

• Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Identyfikatory

DOI

10.4064/cm99-2-1