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Analysis of Heat Equations on Domains. (LMS-31) by El-Maati Ouhabaz

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Chapter Four

UNIFORMLY ELLIPTIC OPERATORS ON DOMAINS

This chapter is devoted to second-order uniformly elliptic operators considered on domains of 411584011and subject to various boundary conditions. We apply the criteria of positivity, L-contractivity, and domination of semi-groups, stated in an abstract setting in the previous chapters, to concrete situations of differential operators. The operators under consideration here may have real-or complex-valued measurable coefficients. The aim is to describe precisely how the above properties of the semigroup depend on the boundary conditions and on the coefficients of the operator.

4.1 EXAMPLES OF BOUNDARY ...

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