Heat Kernel Estimates and LP Spectral Independence of Elliptic Operators |
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Authors: | Kunstmann Peer Christian |
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Institution: | 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 p1, ) 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 p1, ). 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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