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On the domains of elliptic operators in \(L^1\). (English) Zbl 1164.35365

Summary: We prove optimal embedding estimates for the domains of second-order elliptic operators in \(L^1\) spaces. Our procedure relies on general semigroup theory and interpolation arguments, as well as on estimates for \(\nabla T(t)f\) in \(L^1\), in \(L^\infty \), and possibly in fractional Sobolev spaces, for \(f\in L^1\). We provide a number of examples, including some degenerate hypoelliptic operators and operators with unbounded coefficients.

MSC:

35J70 Degenerate elliptic equations
35K65 Degenerate parabolic equations
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