Heat kernels of multiplicative perturbations: Holder estimates and Gaussian lower bounds
El Maati Ouhabaz
47D0647F0547B44semigroupselliptic operatorsGaussian estimates for heat kernels
We study in an abstract setting heat kernels of multiplicative perturbations $bA$ where $b$ is a bounded measurable function. Our aim is to show that H\"older estimates and Gaussian lower bounds carry over from the heat kernel of $A$ to the heat kernel of $bA$. In preparing these results we show that H\"older continuity estimates of heat kernels can be characterized in terms of Gagliardo-Nirenberg type inequalities.
Indiana University Mathematics Journal
1998
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10.1512/iumj.1998.47.1582
10.1512/iumj.1998.47.1582
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Indiana Univ. Math. J. 47 (1998) 1481 - 1496
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