Hardy's inequality for functions vanishing on a part of the boundary

We develop a geometric framework for Hardy's inequality on a bounded domain when the functions do vanish only on a closed portion of the boundary.Comment: 26 pages, 2 figures, includes several improvements in Sections 6-8 allowing to relax the assumptions in the main results. Final version published at http://link.springer.com/article/10.1007%2Fs11118-015-9463-

Gaussian estimates for second order elliptic operators with boundary conditions

We prove Gaussian estimates for the kernel of the semigroup generated by a second order operator A in divergence form with real, not necessarily symmetric, second order coefficients on an open subset $\Omega$ of $\mathbb R^d$ satisfying various boundary conditions. Moreover, we show that A + \omegaI has a bounded $H_\infty$-functional calculus and has bounded imaginary powers if $\omega$ is large enough

Second-order strongly elliptic operators on Lie groups with Hölder continuous coefficients

No displayable abstract

High order divergence-form elliptic operators on Lie groups

We give a straightforward proof that divergence-form elliptic operators of order m on a d-dimensional Lie group with m ≥ d have Hölder continuous kernels satisfying Gaussian bounds

Reduced heat kernels on homogeneous spaces

No displayable abstract