Heat Kernel Bounds for Elliptic Partial Differential Operators in Divergence Form with Robin-Type Boundary Conditions

Fritz Gesztesy (1) , Marius Mitrea (2) , Roger Nichols (3) , El Maati Ouhabaz (4)

1 Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
2 Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
3 Mathematics Department, The University of Tennessee at Chattanooga
4 IMB - Institut de Mathématiques de Bordeaux

The principal aim of this short note is to extend a recent result on Gaussian heat kernel bounds for self-adjoint $L^2(\Om; d^n x)$-realizations, of divergence form elliptic partial differential expressions $L$ with (nonlocal) Robin-type boundary conditions in bounded Lipschitz domains $\Om \subset \bbR^n$.

Mots clés: heat kernel bounds; Green's function bounds; Robin boundary conditions; elliptic partial differential operators; Positivity preserving semigroups

Domaines: Equations aux dérivées partielles [math.AP]

Fritz Gesztesy, Marius Mitrea, Roger Nichols, El Maati Ouhabaz. Heat Kernel Bounds for Elliptic Partial Differential Operators in Divergence Form with Robin-Type Boundary Conditions. Proc. Amer. Math. Soc., 2015, pp.13. ⟨hal-00830563⟩