Continuous solutions of nonlinear Cauchy-Riemann equations and
pseudoholomorphic curves in normal coordinates
Adam Coffman, Yifei Pan, and Yuan Zhang
article abstract
We establish elliptic regularity for nonlinear inhomogeneous
Cauchy-Riemann equations under minimal assumptions, and give a
counterexample in a borderline case. In some cases where the
inhomogeneous term has a separable factorization, the solution set can
be explicitly calculated. The methods also give local parametric
formulas for pseudoholomorphic curves with respect to some continuous
almost complex structures.