Exceptional sets for solutions to subelliptic equations
This paper deals with removable singularities for bounded solutions of the following class of nonlinear hypoelliptic equations: \[ -\sum^m_{j=1} X^*_jA_j(x,u,X_1u,\dots,X_mu)= f(x,u,X_1u,\dots,X_mu), \] where the \(C^\infty\) vector fields \(X_1,\dots,X_m\) fulfill the well-known Hörmander's conditions for hypoellipticity. Sufficient conditions for removability of the singularities of bounded solutions are proved. In a special case these conditions turn out to be necessary, too. An application to some variational problems is given. At the end of the paper it is shown that the capacity of the set on which a solution of the subelliptic equation is \(+\infty\) equals 0.
scientific article; zbMATH DE number 923537
scientific article