Intrinsic Harnack Type Inequalities for Solutions of Certain Degenerate Parabolic Equations
Title | Intrinsic Harnack Type Inequalities for Solutions of Certain Degenerate Parabolic Equations PDF eBook |
Author | E. Di Benedetto |
Publisher | |
Pages | 34 |
Release | 1986 |
Genre | |
ISBN |
Harnack's Inequality for Degenerate and Singular Parabolic Equations
Title | Harnack's Inequality for Degenerate and Singular Parabolic Equations PDF eBook |
Author | Emmanuele DiBenedetto |
Publisher | Springer Science & Business Media |
Pages | 287 |
Release | 2011-11-13 |
Genre | Mathematics |
ISBN | 1461415845 |
Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive overview, that would highlight the main issues and also the problems that still remain open. The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p-laplace and porous medium type equations, both in the degenerate (p/i”2 or im/i”1) and in the singular range (1“ip/i2 or 0“im/i
Harnack's Inequality for Degenerate and Singular Parabolic Equations
Title | Harnack's Inequality for Degenerate and Singular Parabolic Equations PDF eBook |
Author | |
Publisher | |
Pages | 294 |
Release | 2011-11-01 |
Genre | |
ISBN | 9781461415855 |
Degenerate Parabolic Equations
Title | Degenerate Parabolic Equations PDF eBook |
Author | Emmanuele DiBenedetto |
Publisher | Springer Science & Business Media |
Pages | 402 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461208955 |
Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.
Harnack Type Inequalities for Solutions of Certain Doubly Nonlinear Parabolic Equations
Title | Harnack Type Inequalities for Solutions of Certain Doubly Nonlinear Parabolic Equations PDF eBook |
Author | Vincenzo Vespri |
Publisher | |
Pages | 23 |
Release | 1991 |
Genre | Differential equations, Nonlinear |
ISBN |
Harnack Inequalities and Nonlinear Operators
Title | Harnack Inequalities and Nonlinear Operators PDF eBook |
Author | Vincenzo Vespri |
Publisher | Springer Nature |
Pages | 202 |
Release | 2021-05-29 |
Genre | Mathematics |
ISBN | 3030737780 |
The book contains two contributions about the work of Emmanuele DiBenedetto and a selection of original papers. The authors are some of the main experts in Harnack’s inequalities and nonlinear operators. These papers are part of the contributions presented during the conference to celebrate the 70th birthday of Prof. Emmanuele DiBenedetto, which was held at “Il Palazzone” in Cortona from June 18th to 24th, 2017. The papers are focused on current research topics regarding the qualitative properties of solutions, connections with calculus of variations, Harnack inequality and regularity theory. Some papers are also related to various applications. Many of the authors have shared with Prof. DiBenedetto an intense scientific and personal collaboration, while many others have taken inspiration from and further developed his field of research. The topics of the conference are certainly of great interest for the international mathematical community.
Nonlinear Diffusion Equations and Their Equilibrium States I
Title | Nonlinear Diffusion Equations and Their Equilibrium States I PDF eBook |
Author | W.-M. Ni |
Publisher | Springer Science & Business Media |
Pages | 359 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461396050 |
In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = D.u + f(u). Here D. denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium D.u + f(u) = o. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.