Nonlinear Differential Equations

Abstract

In the foregoing Chapter V, we considered a 1inear partial differential operator g of order 2k and constructed a suitable weighted Sobolev space W^k,2(Ω;S) in which some boundary value problem (mainly, the Dirichlet problem) for g was uniquely weakly solvable. The collection S of weight functions wα∈ W(Ω) was determined by the operator or, more precisely, by its coefficients a_αß.