Focusing on the semi-boundedness of partial differential operators, this groundbreaking work presents the authors' original research and insights into varying interpretations of the topic. It delves into function spaces, specifically highlighting the Hilbert and Banach spaces, and explores the implications of these mathematical frameworks. The book contributes significantly to the understanding of this emerging area in mathematics.
This volume features invited lectures from the International Workshop "Analysis, Partial Differential Equations and Applications," held at Sapienza University of Rome to celebrate Vladimir G. Maz'ya's 70th birthday. A distinguished mathematician, Maz'ya is a leading figure in pure and applied analysis. The book seeks to disseminate his influential ideas to a broader audience in science and engineering faculties. Each article draws inspiration from Maz'ya's extensive work across various frameworks, addressing classical and contemporary issues related to boundary and initial value problems for elliptic, hyperbolic, and parabolic operators, as well as Schrödinger-type equations, mathematical elasticity, potential theory, capacity, singular integral operators, p-Laplacians, functional analysis, and approximation theory. With over 450 papers and 20 books to his name, Maz'ya has made significant contributions to the theory of harmonic potentials on non-smooth domains, potential and capacity theories, spaces of functions with bounded variation, and more. This collection will be invaluable for researchers seeking a deeper insight into Maz'ya's vast expertise.
