This book investigates the challenges and solutions for ill-posed variational problems, a class of mathematical problems where solutions do not exist or are not unique. It explores the theoretical underpinnings of these problems, which arise in various scientific and engineering disciplines, and presents a comprehensive overview of regularization techniques designed to approximate stable and meaningful solutions. The work is based on contributions from a workshop, indicating a collection of research perspectives on the subject.

This collection of works, stemming from a dedicated workshop, likely offers a deep dive into advanced mathematical concepts. The focus on variational problems and regularization techniques suggests a text aimed at researchers and advanced students in mathematics, applied mathematics, and related scientific fields. The material is expected to be rigorous, presenting theoretical developments and computational methods for tackling complex, ill-posed mathematical challenges.