Direct and Inverse Problems with Applications

Extended Abstracts of the 2024 GAP Center Summer School
Erscheinungsjahr 2026
ISBN: 978-3-031-98644-4
Verlag: Birkhäuser

Buch, Englisch, 235 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 584 g

Reihe: Trends in Mathematics

This volume presents the extended abstracts from the 2024 Summer School organized by the Ghent Analysis and PDE Center. The school focused on equipping participants with a broad spectrum of mathematical tools for addressing both direct and inverse problems across various fields. Through a combination of lectures, problem-solving sessions, and collaborative discussions, the program fostered the development of innovative methods and techniques. The lectures also include broader related topics in mathematical analysis and partial differential equations, offering a comprehensive perspective on current research directions in the field.

Zielgruppe

Research

Autoren/Hrsg.

Chatzakou, Marianna

Ruzhansky, Michael

Bockstal, Karel van

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

Inhaltsverzeichnis

Fourier algebras and homomorphisms.- Dispersion phenomena and applications to evolution equations.- Subriemannian geometry and analysis of hypoelliptic PDE.- Stability results for Sobolev, logarithmic Sobolev, and related inequalities.- Semiconcavity, viscosity solutions and the square distance in Carnot groups.- Direct and inverse nonstationary scattering problems for Dirac-type system.- Quantitative homogenisation for differential equations with highly anisotropic partially degenerating coefficients.- Rigidity results for evolution PDEs on homogeneuos Lie groups.- An overview of dualities in non-commutative harmonic analysis.- Colombeau type extensions, assymptotic scales.- Analytical solutions to the Laplace equation on a hemispherical domain.- Uniform spectral asymptotics for high-contrast periodic media.- Asymptotic mean value formulas for the -Laplacian in the Euclidean space and in the Heisenberg Group.- Global solutions for a class of nonlinear evolution equations in supercritical spaces.- An index transform method for solutions of the boundary value problems in a wedge.

Über Autor(innen)

Mariana Chatzakou is a postdoctoral researcher at Ghent University, Belgium. 

Michael Ruzhansky is a senior full professor of Mathematics at Ghent University in Belgium, and a professor of Mathematics at Queen Mary University of London in the United Kingdom. 

Karel Van Bockstal is a postdoctoral researcher at Ghent University, Belgium.