2012/11/15 by Katharine A. Ott, Katharine Ott, Russell M. Brown +1 · 8 citations
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Boundary value problem #Bounded function #Combinatorics #Dirichlet problem #Disjoint sets #Domain (mathematical analysis) #Exponent #Hardy space #Lipschitz continuity #Lipschitz domain #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Omega #Pure mathematics #Sobolev space #math.AP #msc:35J25
paper · pdf · doi:10.1016/j.jde.2013.03.007
published in Journal of Differential Equations 254(12), 4373-4400 (Elsevier BV)
arxiv created 2012/11/15 · openalex publication_date 2013/04/06 · arxiv updated 2013/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the mixed problem for L the Lamé system of elasticity in a bounded Lipschitz domain Ω⊂\reals 2. We suppose that the boundary is written as the union of two disjoint sets, ∂Ω=D∪ N. We take traction data from the space Lp(N) and Dirichlet data from a Sobolev space W1,p(D) and look for a solution u of Lu =0 with the given boundary conditions. We give a scale invariant condition on D and find an exponent p0 >1 so that for 1<p<p0, we have a unique solution of this boundary value problem with the non-tangential maximal function of the gradient of the solution in L^ p(∂Ω). We also establish the existence of a unique solution when the data is taken from Hardy spaces and Hardy-Sobolev spaces with p in (p1,1] for some p1 <1.