Moduli space, Lecture 3

21 Janeiro 2022, 10:00 • Davide Masoero

We study the solvability of the Beltrami equation in case of coefficients with different types of regularity (smooth, measurable and essentially bounded). We prove the existence and uniqueness of a solution in the Sobolev space W^{1,2}_loc(C) in the case of Beltrami essentially bounded coefficients with compact support. Partial results are given, in order to improve the regularity class of this solution in case of smooth coefficients.