Solutions for quasilinear nonsmooth evolution systems in L^p

We prove that nonsmooth quasilinear parabolic systems admit a local, strongly differentiable (with respect to time) solution in Lp over a bounded three-dimensional polyhedral space domain. The proof rests essentially on new elliptic regularity results for polyhedral Laplace interface problems with anisotropic materials. These results are based on sharp pointwise estimates for Green's function, which are also of independent interest. To treat the nonlinear problem, we then apply a classical theorem of Sobolevskii for abstract parabolic equations and recently obtained resolvent estimates for elliptic operators and interpolation results. As applications we have in mind primarily reaction diffusion systems. The treatment of such equations in an Lp context seems to be new and allows (by Gauss' theorem) to define properly the normal component of currents across the boundary

Splines and local approximation of the earth's gravity field

Bibliography: pages 214-220.The Hilbert space spline theory of Delvos and Schempp, and the reproducing kernel theory of L. Schwartz, provide the conceptual foundation and the construction procedure for rotation-invariant splines on Euclidean spaces, splines on the circle, and splines on the sphere and harmonic outside the sphere. Spherical splines and surface splines such as multi-conic functions, Hardy's multiquadric functions, pseudo-cubic splines, and thin-plate splines, are shown to be largely as effective as least squares collocation in representing geoid heights or gravity anomalies. A pseudo-cubic spline geoid for southern Africa is given, interpolating Doppler-derived geoid heights and astro-geodetic deflections of the vertical. Quadrature rules are derived for the thin-plate spline approximation (over a circular disk, and to a planar approximation) of Stokes's formula, the formulae of Vening Meinesz, and the L₁ vertical gradient operator in the analytical continuation series solution of Molodensky's problem

Radial basis function methods for multivariable approximation

Digitisation of this thesis was sponsored by Arcadia Fund, a charitable fund of Lisbet Rausing and Peter Baldwin

The heat kernel for manifolds with conic singularities

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.Includes bibliographical references (p. 81).by Edith Mooers.Ph.D