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Elliptic boundary value problems in non-smooth domains via a harmonic analysis and geometric measure theory approach

Grant number: 16/22593-1
Support type:Research Grants - Visiting Researcher Grant - International
Duration: February 04, 2017 - February 12, 2017
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Gustavo Hoepfner
Grantee:Gustavo Hoepfner
Visiting researcher: Marius Mitrea
Visiting researcher institution: University of Missouri, Columbia (UM), United States
Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
Associated research grant:12/03168-7 - Geometric theory of PDE and several complex variables, AP.TEM

Abstract

This research proposal is envisioned as a collaborative effort between faculty members Gustavo Hoepfner (Universidade Federal de São Carlos), Paulo Liboni (Universidade Estadual de Londrina), Irina Mitrea (Temple University) and Marius Mitrea (University of Missouri-Columbia). The three main research directions of this proposal, rooted in the areas of Harmonic Analysis (HA), Geometric Measure Theory (GMT) and Partial Differential Equations (PDE), are: A. Develop a new generation of Calderón-Zygmund theory for multi-layer potential operators in uniformly rectifiable (UR) domains. This includes mapping properties, non-tangential maximal function estimates, and Carleson measure estimates for multi-layers of double and single type in UR domains; B. Identify algebraic and geometric measure theoretic settings for which boundary multi-layer potential operators of double and single type are invertible on appropriate function spaces on the boundary suitably adapted to the higher order setting; C. Establish spectral properties of layer potentials associated with second and higher order elliptic problems in UR domains. (AU)

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