Heat Kernel Estimates and LP Spectral Independence of Elliptic Operators |
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Authors: | Kunstmann Peer Christian |
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Affiliation: | Mathematisches Institut I, Universität Karlsruhe Englerstr. 2, D76128 Karlsruhe, Germany |
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Abstract: | Let be an open subset of Rd, and let Tp for p[1, ) be consistentC0-semigroups given by kernels that satisfy an upper heat kernelestimate. Denoting their generators by Ap, we show that thespectrum (Ap) is independent of p[1, ). We also treat the caseof weighted Lp-spaces for weights that satisfy a subexponentialgrowth condition. An example shows that independence of thespectrum may fail for an exponential weight. 1991 MathematicsSubject Classification 47D06, 47A10, 35P05. |
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