34 research outputs found
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 of satisfying various boundary conditions. Moreover, we show that A + \omegaI has a bounded -functional calculus and has bounded imaginary powers if 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