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Nonlinear Partial Differential Equations

Date: September 26, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Giles Auchmuty, University of Houston

  

Title: Nonlinear PDEs Seminar

Abstract:

Title: Energy Bounds for Planar Div-curl Boundary Value Problems

Abstract: This talk will describe the derivation of sharp L^2 norm estimates for the solutions of div-curl boundary value problems on bounded Lipschitz planar regions Nontrivial prescribed tangential, normal or mixed boundary condition problems are considered of the type that arise in stationary electromagnetic eld modeling. The solutions are found using special decompositions of the vector elds in terms of scalar potentials, stream functions and harmonic elds. Explicit spectral formulae for the solutions are derived that involve various eigenvalues and eigenfunctions of the Laplacian including the Steklov eigenvalues and eigenfunctions. The bounds depend on certain least eigenvalues and the given data.