Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials

This paper studies second order elliptic equations in both divergence and non-divergence forms with measurable complex valued principle coefficients potentials. The PDE operators can be considered as generalized Schrodinger operators. Under some sufficient conditions, we prove existence, uniqueness, regularity estimates Sobolev spaces for solutions to the equations. We particularly show that non-zero imaginary parts of potentials are main mechanisms control solutions. Our results limiting absorption they could useful applications. approach is based on perturbation technique freezes not only generalize known but also provide a key ingredient study \begin{document}$ L^p $\end{document} -diffusion phenomena dissipative wave