On a class of higher-order operators with complex coefficients, elliptic in the sense of G√•rding’s inequality. (English) Zbl 1073.35076

Summary: We study a class of higher-order elliptic operators in divergence form with nonsmooth, complex coefficients independent of time. In particular, we give some elliptic regularity results for weak solutions and establish upper bounds for higher derivatives of the heat kernel associated to this class of operators.


35J30 Higher-order elliptic equations
35J45 Systems of elliptic equations, general (MSC2000)
35A08 Fundamental solutions to PDEs
35K25 Higher-order parabolic equations
35K40 Second-order parabolic systems