Continuous solutions of nonlinear Cauchy-Riemann equations and   pseudoholomorphic curves in normal coordinates
  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. 
Adam Coffman, Yifei Pan, Yuan Zhang
math.CV math.AP