Analysis, Partial Differential Equations and Applications

This volume includes several invited lectures given at the International Workshop "Analysis, Partial Differential Equations and Applications", held at the Mathematical Department of Sapienza University of Rome, on the occasion of the 70th birthday of Vladimir G. Maz'ya, a renowned mathematician and one of the main experts in the field of pure and applied analysis.

The book aims at spreading the seminal ideas of Maz'ya to a larger audience in faculties of sciences and engineering. In fact, all articles were inspired by previous works of Maz'ya in several frameworks, including classical and contemporary problems connected with boundary and initial value problems for elliptic, hyperbolic and parabolic operators, Schrödinger-type equations, mathematical theory of elasticity, potential theory, capacity, singular integral operators, p-Laplacians, functional analysis, and approximation theory.

Maz'ya is author of more than 450 papers and 20 books. In his long career he obtained many astonishing and frequently cited results in the theory of harmonic potentials on non-smooth domains, potential and capacity theories, spaces of functions with bounded variation, maximum principle for higher-order elliptic equations, Sobolev multipliers, approximate approximations, etc. The topics included in this volume will be particularly useful to all researchers who are interested in achieving a deeper understanding of the large expertise of Vladimir Maz'ya.

Inhalt
On the Occasion of the 70th Birthday of Vladimir Maz'ya.- Boundary Trace for BV Functions in Regions with Irregular Boundary.- Dirac Equation as a Special Case of Cosserat Elasticity.- Hölder and Lipschitz Estimates for Viscosity Solutions of Some Degenerate Elliptic PDE's.- Criteria for the L p -dissipativity of Partial Differential Operators.- Sharp Estimates for Nonlinear Potentials and Applications.- Solvability Conditions for a Discrete Model of Schrödinger's Equation.- An Algebra of Shift-invariant Singular Integral Operators with Slowly Oscillating Data and Its Application to Operators with a Carleman Shift.- Frozen History: Reconstructing the Climate of the Past.- Multidimensional Harmonic Functions Analogues of Sharp Real-part Theorems in Complex Function Theory.- Cubature of Integral Operators by Approximate Quasi-interpolation.- Pointwise Estimates for the Polyharmonic Green Function in General Domains.- On Elliptic Operators in Nondivergence and in Double Divergence Form.- On the Well-posedness of the Dirichlet Problem in Certain Classes of Nontangentially Accessible Domains.- On Negative Spectrum of Schrödinger Type Operators.- ACL-homeomorphisms in the Plane.- Crack Problems for Composite Structures.- On Positive Solutions of p-Laplacian-type Equations.- Mixed Boundary Value Problems for Stokes and Navier-Stokes Systems in Polyhedral Domains.- On Some Classical Operators of Variable Order in Variable Exponent Spaces.- Irregular Conductive Layers.- On the Double Layer Potential.