Let A be a real symmetric, degenerate elliptic matrix whose degen- eracy is controlled by a weight w in the A2 or QC class, or let A be a smooth imaginary perturbation of such a matrix. We show that there is a heat kernel Wt (x, y) associated to the parabolic equation wut = −divA∇u, and Wt satisfies a certain Gaussian bound. We then use this bound to derive a number of other properties of the kernel.
The Kato problem for degenerate elliptic operators / Fiorenza, Alberto; Sbordone, Carlo. - (2009).
The Kato problem for degenerate elliptic operators
FIORENZA, ALBERTO;SBORDONE, CARLO
2009
Abstract
Let A be a real symmetric, degenerate elliptic matrix whose degen- eracy is controlled by a weight w in the A2 or QC class, or let A be a smooth imaginary perturbation of such a matrix. We show that there is a heat kernel Wt (x, y) associated to the parabolic equation wut = −divA∇u, and Wt satisfies a certain Gaussian bound. We then use this bound to derive a number of other properties of the kernel.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
