## Heat kernel estimates for operators with boundary conditions.(English)Zbl 0973.35087

The paper deals with heat kernels associated with second-order parabolic operators with measurable bounded coefficients on domains in $${\mathbb{R}}^N$$ subject to various types of boundary conditions. Based on the variational setting the author develops a unified approach to the $$L_p$$-theory of the corresponding evolution systems. Gaussian type upper bounds on the heat kernels are derived using Nash type inequalities and Davies’ perturbation techniques.

### MSC:

 35K20 Initial-boundary value problems for second-order parabolic equations 35B45 A priori estimates in context of PDEs
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### References:

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