## 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