Geometric methods in PDE's

✍ Scribed by Giovanna Citti, Maria Manfredini, Daniele Morbidelli, Sergio Polidoro, Francesco Uguzzoni (eds.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 381
• Series: Springer INdAM series volume 13
• Edition: 1st ed.
• Category: Library

✦ Synopsis

The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications. 

✦ Table of Contents

Front Matter....Pages i-xiii
On Friedrichs Commutators Lemma for Hardy Spaces and Applications....Pages 1-14
On the Hardy Constant of Some Non-convex Planar Domains....Pages 15-41
Sharp Singular Trudinger-Moser-Adams Type Inequalities with Exact Growth....Pages 43-80
A Quantitative Lusin Theorem for Functions in BV....Pages 81-87
X-Elliptic Harmonic Maps....Pages 89-109
Sum Operators and Fefferman–Phong Inequalities....Pages 111-120
L p -Parabolic Regularity and Non-degenerate Ornstein-Uhlenbeck Type Operators....Pages 121-139
Local Solvability of Nonsmooth Hörmander’s Operators....Pages 141-157
Multiple Solutions for an Eigenvalue Problem Involving Non-local Elliptic p-Laplacian Operators....Pages 159-176
Uniqueness of Solutions of a Class of Quasilinear Subelliptic Equations....Pages 177-198
Liouville Type Theorems for Non-linear Differential Inequalities on Carnot Groups....Pages 199-214
Modica Type Gradient Estimates for Reaction-Diffusion Equations....Pages 215-242
A Few Recent Results on Fully Nonlinear PDE’s....Pages 243-255
Hölder Regularity of the Gradient for Solutions of Fully Nonlinear Equations with Sub Linear First Order Term....Pages 257-268
The Reflector Problem and the Inverse Square Law....Pages 269-286
Gagliardo-Nirenberg Inequalities for Horizontal Vector Fields in the Engel Group and in the Seven-Dimensional Quaternionic Heisenberg Group....Pages 287-312
Regularity of the Free Boundary in Problems with Distributed Sources....Pages 313-340
The Role of Fundamental Solution in Potential and Regularity Theory for Subelliptic PDE....Pages 341-373

✦ Subjects

Fourier analysis;Functional analysis;Differential equations, Partial;Potential theory (Mathematics);Geometry, Differential;Calculus of variations;Mathematics