1 edition of **Harnack"s Inequality for Degenerate and Singular Parabolic Equations** found in the catalog.

Harnack"s Inequality for Degenerate and Singular Parabolic Equations

Emmanuele DiBenedetto

- 359 Want to read
- 40 Currently reading

Published
**2012**
by Springer Science+Business Media, LLC in New York, NY
.

Written in English

- Mathematics,
- Global analysis (Mathematics),
- Partial Differential equations,
- Analysis,
- Special Functions

**Edition Notes**

Statement | by Emmanuele DiBenedetto, Ugo Gianazza, Vincenzo Vespri |

Series | Springer Monographs in Mathematics |

Contributions | Gianazza, Ugo, Vespri, Vincenzo, SpringerLink (Online service) |

The Physical Object | |
---|---|

Format | [electronic resource] / |

ID Numbers | |

Open Library | OL25570400M |

ISBN 10 | 9781461415831, 9781461415848 |

Scholes equations in [18]) are described by degenerate parabolic equations. On the other hand, the elds of applications of Carleman estimates in studying controllability and inverse problems for degenerate parabolic coupled systems are Mathematics Subject Classi cation. 35K65, 35K40, 35B45, 93B05, 93B Key words and phrases. Author: William Schmidt Publisher: Teachers College Press ISBN: Size: MB Format: PDF, ePub, Docs View: Get Books. Inequality For All Inequality For All by William Schmidt, Inequality For All Books available in PDF, EPUB, Mobi Format. Download Inequality For All books, Inequality for All makes an important contribution to current debates about economic inequalities .

Equation () reflects the more practical process of heat conduction than the classical heat conduction equation u t = Δ u does. For example, when p > 2, the solution of the equation may possess the property of propagation of finite speed, while u t = Δ u always has the property of propagation of infinite speed which seems clearly contrary to the practice.. There is a tremendous . Degenerate and Singular Differential Operators with Applications to Boundary Value Problems On the Time Periodic Free Boundary Associated to Some Nonlinear Parabolic Equations. We give sufficient conditions, being also necessary in many cases, for the existence of a periodic free boundary generated as the boundary of the support of the.

of homogeneity of parabolic systems with p-growth when p = 2. They came up with a sort of reverse-type Holder inequality. The new ingredient offered by these¨ authors is a suitable application of DiBenedetto’s intrinsic geometry method for de-generate/singular parabolic systems (see [8]) in the setting of Gehring-type estimates. In the whole space, Kartsatos studied a Liouville type theorem on the solution for a quasi-linear parabolic equation without singular variable coefficient and gradient term. For a more general evolution and quasi-linear parabolic type inequality, see [7, 8] and references therein.

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From the reviews:"Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years, but the issue of the Harnack inequality has remained basically open.

In the Introduction to this monograph, the authors present the history of the subject beginning with Harnack's inequality for nonnegative harmonic.

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 ly considerable progress has been made on this Price: $ The authors treat the Harnack inequality for nonnegative solutions to p-Laplace and porous medium type equations, both in the degenerate and in the singular range.

The work is mathematical in nature; its aim is to introduce a novel set of tools and techniques that deepen our understanding of the notions of degeneracy and singularity in partial.

The p-Laplacian has been widely studied as a standard model for elliptic and parabolic equations with degenerate-singular diffusion, and appears in a wide number of physical applications (see for. DiBenedetto / Gianazza / Vespri, Harnack's Inequality for Degenerate and Singular Parabolic Equations,Buch, Bücher schnell und portofrei Beachten Sie bitte die aktuellen Informationen unseres Partners DHL zu Liefereinschränkungen im Ausland.

Books About Harnack's Estimates: Positivity and Local Behavior of Degenerate and Singular Parabolic Equations. Authors: Emmanuele DiBenedetto, Ugo Gianazza, Reverse Smoothing Effects, Fine Asymptotics, and Harnack Inequalities for Fast Diffusion Equations. Cite this chapter as: DiBenedetto E., Gianazza U., Vespri V.

() The Harnack Inequality for Degenerate Equations. In: Harnack's Inequality for Degenerate and Singular Parabolic Equations. The equations we consider include uniformly elliptic equations and linearized Monge–Ampère equations.

Our argument allows us to prove the doubling estimate for functions which, at points of large gradient, are solutions of (degenerate and singular) elliptic equations with unbounded drift. 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. Page - YZ Chen and E.

DiBenedetto, On the Harnack inequality for non-negative solutions of singular parabolic equations, Proc. of Conf. Non-linear diffusion, in Honour of J. Appears in 3 books. BOUNDARY ESTIMATES FOR SINGULAR EQUATIONS OF p-PARABOLIC TYPE 3 Rn+1 +:= Rn + R = f(x 1;;x n;t) 2Rn R: x >0g.

Since u= x is solution to the p-parabolic equation in Rn+1 +, and since u= x n vanishes continuously on the boundary of Rn+1 +, it is obvious that in the degenerate case two non-negative solutions to the p-parabolic equation in Rn+1 + need not have the same decay at the.

Preliminaries.- 3. Degenerate and Singular Parabolic Equations.- 4. Expansion of Positivity.- 5. The Harnack Inequality for Degenerate Equations.- 6.

The Harnack Inequality for Singular. Savin used the idea of applying the equation at contact points with paraboloids in to prove an ABP-type measure estimate.

Wang subsequently adapted this to the parabolic setting in. It seems hopeful that our technique can also be adapted to prove an analogous measure estimate for a class of degenerate parabolic equations.

Nonlinear Analysis, Theory, Methods & Applications, Vol. 17, No. 11, pp.X/91 $+ Printed in Great Britain. Pergamon Press plc Ll-ESTIMATES FOR DEGENERATE AND SINGULAR PARABOLIC EQUATIONS MARIA MICHAELA PORZIO* Department of Mathematics, Northwestern University, Evanston, ILU.S.A.

(Received 21 May. In the above inequality we used that on @[email protected] we have u= 0, by the de nition of Uand the continuity of u. Lastly, we trivially have max nU u 0 max @ u+ which concludes the proof. 3 Strong maximum principle The strong maximum principle tells us that for a solution of an elliptic equation, extrema can be attained in the interior if and only if the.

The Harnack inequality is tightly related to Holder estimates for solutions to elliptic/parabolic equations. For a large class of problems both statements are equivalent. But there are simple cases (stable processes with the spectral measure consisting of atoms) where the Harnack inequality fails but Hölder estimates still hold true.

() Improved Hardy-Poincaré inequalities and sharp Carleman estimates for degenerate/singular parabolic problems. Discrete and Continuous Dynamical Systems - Series S() Sharp Carleman estimates for singular parabolic equations and application to Lipschitz stability in inverse source problems.

In the Euclidean space, regularity to elliptic and parabolic equations and systems has been studied by many authors (see [1,2,3,4,5,6,7,8] and the references therein).

Giaquinta in [ 5 ] proved the reverse Hölder estimates for weak solutions to diagonal elliptic systems with Hölder continuous coefficients and obtained the higher integrability.

Vancostenoble, Improved Hardy-Poincare inequalities and sharp Carleman estimates for degenerate/singular parabolic problems.

Discrete Contin. Dyn. Syst. Ser.S 4 (), Google Scholar Cross Ref; J. Vancostenoble and E. Zuazua, Null controllability for the heat equation with singular inverse-square potentials.

() Improved Hardy-Poincaré inequalities and sharp Carleman estimates for degenerate/singular parabolic problems. Discrete and Continuous Dynamical Systems - Series S() Determination of source terms in a degenerate parabolic equation.

Citation: Giuseppe Di Fazio, Maria Stella Fanciullo, Pietro Zamboni. Harnack inequality for degenerate elliptic equations and sum operators.

Communications on Pure & Applied Analysis,14 (6): doi: /cpaa Gutiérrez CrE, Wheeden RL: Harnack's inequality for degenerate parabolic equations.

Communications in Partial Differential Equations ,16() / MATH MathSciNet Google Scholar. Maximum principles are bedrock results in the theory of second order elliptic equations.

This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their Reviews: 1.