On a priori energy estimates for characteristic boundary value problems (Q485265)

Motivated by the study of certain nonlinear free-boundary value problems for hyperbolic systems of partial differential equations arising in magneto-hydrodynamics, in this paper the authors show that an a priori estimate of the solution to certain boundary value problems, in the conormal Sobolev space \(H^{1}_{\mathrm{tan}}\), can be transformed into an \(L^{2}\) a priori estimate of the same problem.