Svitlana Mayboroda's Books

This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Lp classes. The authors establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given Lp space automatically assures their solvability in an extended range of Besov spaces; (3) Well-posedness for the non-homogeneous boundary value problems. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.

We study a variant of the Alt, Caffarelli, and Friedman free boundary problem, with many phases and a slightly different volume term, which we originally designed to guess the localization of eigenfunctions of a Schrödinger operator in a domain. We prove Lipschitz bounds for the functions and some nondegeneracy and regularity properties for the domains"--Abstract.

Book's by Svitlana Mayboroda

Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces

Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces

Elliptic Theory for Sets with Higher Co-Dimensional Boundaries

Elliptic Theory for Sets with Higher Co-Dimensional Boundaries

Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces

Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces

Elliptic Theory for Sets with Higher Co-Dimensional Boundaries

Elliptic Theory for Sets with Higher Co-Dimensional Boundaries

A Free Boundary Problem for the Localization of Eigenfunctions

A Free Boundary Problem for the Localization of Eigenfunctions

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