7. A Model Fourth-Order Problem
Society for Industrial and Applied Mathematics eBooks · 2011
7.1 Introductory results In this chapter we shall study the properties of the solutions of the first boundary value problem for the biharmonic operator in a plane domain with a polygonal boundary. All the notation concerning the domain Ω will be the same as in Chapter 4. Our main goal is this: Given with , , we look for a solution of Δ2u=ƒinΩγju=0onΓj,j=1,2,…,Nγj∂u∂vj=0onΓj,j=1,2,…,N.7,1,1 The reason why it is useful to consider ƒ given in will appear clearly in Section 7.4, which is devoted to the related Stokes problem.