Smoothness of solutions to the generalized Dirichlet problem and the eigenvalue problem for differential operators generated by noncoercive bilinear forms (Q1360734)

The author investigates existence, uniqueness, and regularity questions for a generalized Dirichlet problem of the form \[ a[u,v]+ \lambda(u,v)= (F,v),\quad \forall v\in C^\infty_0 (\Omega). \] Here, \(a[\cdot, \cdot]\) is a bilinear form which is not necessarily coercive and the solution \(u\) is shown to exist in a weighted Sobolev space.