Emmanuele DiBenedetto

Centennial Professor of Mathematics
Department of Mathematics
Vanderbilt University
E-mail: em.diben@vanderbilt.edu
Page: http://www.math.vanderbilt.edu/~dibe/

 

Fields of interest:

Partial Differential Equations of Elliptic and Parabolic Type

Degenerate and Singular Equations

Local and Global Behaviour of Solutions

Harnack-Type Estimates

Calculus of Variations

Quasi-Minima

Potential Theory

Phase Transition

Free Boundary Problems

Fluid Dynamics

Conduction-Convection

Navier Stokes Equations

Motion in Porous Media

Ill-Posed Problems

Thin Film Dynamics

Classical Mechanics

 

Recent publications:

E. DiBenedetto, U. Gianazza and V. Vespri:
Liouville-Type Theorems for Certain Degenerate and Singular Parabolic Equations,
Comptes Rendus Acad. des Sciences ParisSer.I, 348, (2010), 873-877.

E. DiBenedetto, U. Gianazza and V. Vespri:
A New Approach to the Expansion of the Positivity Set of Non-Negative Solutions to Certain Singular Parabolic Partial Differential Equations,
Proc. AMS 138(10) (2010), 3521-3529.

E. DiBenedetto, U. Gianazza and V. Vespri:
Harnack Type Estimates and Holder Continuity for Non-Negative Solutions to Certain Sub-Critically Singular Parabolic Partial Differential Equations,
Manuscripta Mathematica 131 (2010), 231-245.

E. DiBenedetto, U. Gianazza and V. Vespri:
Alternative Forms of the Harnack Inequality for Non-Negative Solutions to Certain Degenerate and Singular Parabolic Equations,
Rend. Accad. Naz. Lincei 20 (2009), 369-377.

E. DiBenedetto, U. Gianazza and V. Vespri:
Continuity of the Saturation in the Flow of two Immiscible Fluids in a Porous Medium,
Indiana Univ. Math. Journal (in press).

E. DiBenedetto, U. Gianazza and V. Vespri:
Sub-Potential Lower Bounds for Non-Negative Solutions to Certain Quasi-Linear Degenerate Parabolic Equations,
Duke Mathematical Journal 143(1) (2008), 1-15.

E. DiBenedetto, U. Gianazza and V. Vespri:
Intrinsic Harnack Estimates for Non-Negative Solutions of Quasilinear Degenerate Parabolic Equations,
Acta Mathematica 200 (2008), 181-209.

E. DiBenedetto, U. Gianazza and V. Vespri:
Local Clustering of the Non-Zero Set of Functions in W1,1,
Rend. Accad. Naz. Lincei 17(2006), 223-225.

D. Andreucci, E. DiBenedetto and P. Bisegna:
Homogenization and Concentrated Capacity for the Heat Equation with non Linear Variational Data in Reticular Almost Disconnected Structures, and Applications to Visual Transduction,
Annali di Matematica Pura e Applicata 182(4) (2003), 375-407.

D. Andreucci, E. DiBenedetto and P. Bisegna:
Homogenization and Concentrated Capacity in Reticular Almost Disconnected Structures,
Comptes Rendus Acad. des Sciences ParisSer. I 335(4) (2002), 329-332.