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 text pdf 10.1512/iumj.1998.47.1582 10.1512/iumj.1998.47.1582 en Indiana Univ. Math. J. 47 (1998) 1481 - 1496 state-of-the-art mathematics http://iumj.org/access/