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Maximal regularity in \(L^p(\mathbb R^N)\) for a class of elliptic operators with unbounded coefficients. (English) Zbl 1174.35394

Summary: Strongly elliptic differential operators with (possibly) unbounded lower-order coefficients are shown to generate \(C_0\) semigroups on \(L^p(\mathbb R^N)\), \(1<p<+\infty \). An explicit characterization of the domain is given.

MSC:

35J70 Degenerate elliptic equations
35K15 Initial value problems for second-order parabolic equations
35K65 Degenerate parabolic equations
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