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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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