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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Solutions To The LP Mixed Boundary Value Problem In C1,1 Domains, Laura D. Croyle
Solutions To The LP Mixed Boundary Value Problem In C1,1 Domains, Laura D. Croyle
Theses and Dissertations--Mathematics
We look at the mixed boundary value problem for elliptic operators in a bounded C1,1(ℝn) domain. The boundary is decomposed into disjoint parts, D and N, with Dirichlet and Neumann data, respectively. Expanding on work done by Ott and Brown, we find a larger range of values of p, 1 < p < n/(n-1), for which the Lp mixed problem has a unique solution with the non-tangential maximal function of the gradient in Lp(∂Ω).
The Bourgain Spaces And Recovery Of Magnetic And Electric Potentials Of Schrödinger Operators, Yaowei Zhang
The Bourgain Spaces And Recovery Of Magnetic And Electric Potentials Of Schrödinger Operators, Yaowei Zhang
Theses and Dissertations--Mathematics
We consider the inverse problem for the magnetic Schrödinger operator with the assumption that the magnetic potential is in Cλ and the electric potential is of the form p1 + div p2 with p1, p2 ∈ Cλ. We use semiclassical pseudodifferential operators on semiclassical Sobolev spaces and Bourgain type spaces. The Bourgain type spaces are defined using the symbol of the operator h2Δ + hμ ⋅ D. Our main result gives a procedure for recovering the curl of the magnetic field and the electric potential from the Dirichlet to Neumann …
Homogenization Of Stokes Systems With Periodic Coefficients, Shu Gu
Homogenization Of Stokes Systems With Periodic Coefficients, Shu Gu
Theses and Dissertations--Mathematics
In this dissertation we study the quantitative theory in homogenization of Stokes systems. We study uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L∞ estimates for the pressure as well as Liouville property for solutions in ℝd. We are able to obtain the boundary W{1,p} estimates in a bounded C1 domain for any 1 < p < ∞. We also study the convergence rates in L2 and H1 of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.
Inverse Scattering For The Zero-Energy Novikov-Veselov Equation, Michael Music
Inverse Scattering For The Zero-Energy Novikov-Veselov Equation, Michael Music
Theses and Dissertations--Mathematics
For certain initial data, we solve the Novikov-Veselov equation by the inverse scat- tering method. This is a (2+1)-dimensional completely integrable system that gen- eralizes the (1+1)-dimensional Korteweg-de-Vries equation. The method used is the inverse scattering method. To study the direct and inverse scattering maps, we prove existence and uniqueness properties of exponentially growing solutions of the two- dimensional Schrodinger equation. For conductivity-type potentials, this was done by Nachman in his work on the inverse conductivity problem. Our work expands the set of potentials for which the analysis holds, completes the study of the inverse scattering map, and show that …