Dissertation - MTH6999
Recent publications
- Regularity of ∞ for Elliptic Equations with Measurable
Coefficients and Its Consequences, Discrete and Continuous Dynamical Systems - Series A (DCDS-A),
32, 10(2012);
arXiv:1010.4263v1.
- Wiener's Criterion at ∞ for the Heat equation and its Measure-theoretical Counterpart,
Electronic Research Announcements in Mathematical Sciences, 15 (2008), 44-51.
- Wiener's Criterion at ∞ for the Heat Equation,
Advances in Differential Equations, 13, 5-6(2008), 457-488.
- Wiener's criterion for the unique solvability of the Dirichlet problem in arbitrary open sets
with non-compact boundaries,
Nonlinear Analysis, 67, 2(2007), 563-578.
- Reaction-diffusion in nonsmooth and closed domains,
Boundary Value Problems, Special issue: Harnack estimates,
Positivity and Local Behaviour of Degenerate and Singular Parabolic
Equations, Vol. 2007 (2007).
- Necessary and sufficient condition for the existence af a unique solution to the first boundary
value problem for the diffusion equation in unbounded domains,
Nonlinear Analysis, 64, 5(2006), 1012-1017.
- Well-posedness of the Dirichlet problem for the nonlinear diffusion equation in non-smooth domains,
Transactions
of Amer. Math. Soc., 357, 1, 2005, 247-265.
- Multidimensional Kolmogorov-Petrovsky test for the boundary regularity
and irregularity of solutions to the heat equation,
Boundary Value Problems, 2, 2005, 181-199.
- Kolmogorov problem for the heat equation and its probabilistic counterpart,
Nonlinear Analysis, 63, 5-7, 2005, 712-724.
- First boundary value problem
for the diffusion equation. I.Iterated logarithm test for the boundary regularity and solvability,
SIAM J. Math. Anal., 34, 6, 2003, 1422-1434.
- Evolution of interfaces and explicit asymptotics at infinity for the fast diffusion equation
with absorption,
Nonlinear Analysis, 50, 4, 2002, 541-560.
- Nonlinear diffusion in irregular domains, in Elliptic and Parabolic Problems, Rolduc and Gaeta 2001, World Scientific, 2002, pp.302-310. PDF
- On the Dirichlet problem for the nonlinear diffusion equation in non-smooth domains,
J. Math. Anal. Appl., 246, 2, 2001, 384-403.
- On the Dirichlet problem for the reaction-diffusion equations in non-smooth domains, Nonlinear Analysis, 47, 2, 2001, 765-776. PDF
- Reaction-diffusion in irregular domains,
J. Differential Equations, 164, 2000, 321-354.
- Interface development and local solutions to reaction-diffusion equations (together with J.R.King),
SIAM J. Math. Anal., 32, 2, 2000, 235-260.
- Reaction-diffusion in a closed domain formed by irregular curves,
J. Math. Anal. Appl., 246, 2000, 480-492.
- Local structure of solutions of the Dirichlet problem for N-dimensional reaction-diffusion equations
in bounded domains, Advances in Differential Equations, 4, 1999, 197-224.
|
Recent preprints
- On the Optimal Control of the Free Boundary Problems for the Second Order Parabolic Equations.
I.Well-posedness and Convergence of the Method of Lines,
arXiv:1203.4866v1.
|
Recent Conferences
|
Minisymposium
Recent Advances in
Partial Differential Equations
March 10-11, 2012
Tampa, Florida
Special Session on
Inverse Problems in
Partial Differential Equations
Special Session on |
Nonlinear
Partial Differential Equations and Applications
November 14-17, 2011
San Diego, California
Minisymposium: Recent Development in Potential Theory, Harmonic Analysis and PDEs
Part I,
Part II
December 10-12, 2007
Mesa, Arizona
Minisymposium: Recent Development in the Theory of Nonlinear
Degenerate Elliptic and Parabolic Equations, Potential Theory and Applications
Part I,
Part II
November 3-4, 2007
Murfreesboro, Tennessee
Special Session on
Nonlinear Partial Differential
Equations and Applications
July 10-12, 2006
Boston Park Plaza Hotel and Towers,
Boston, Massachusetts
Being held jointly with the SIAM Annual Meeting |
Minisymposium Recent Development in the Theory of Nonlinear
Degenerate Elliptic and Parabolic Equations with Applications |
|
Selected recent invited lectures
| Wiener Test at ∞ for Elliptic and Parabolic PDEs, and its Measure-Theoretical, Topological,
and Probabilistic Consequences |
Colloquium lecture, Worcester Polytechnic Institute, Worcester, 16 March, 2012- Wiener's Criterion for the Regularity of ∞ for the Elliptic and Parabolic
Equations and its Measure-theoretical Counterpart, PDE Seminar,
University of Pittsburgh, 1 November, 2007
- Elliptic and Parabolic Problems in Domains with Noncompact Boundaries, PDE Seminar, Ohio State University, Columbus, 1 March, 2006
- Parabolic Problems in Non-smooth Domains with Applications, Biomathematics and Analysis
Seminar, Vanderbilt University, Nashville, 9 February, 2005
- Boundary Regularity and Irregularity for the Diffusion Equation and its Brownian Motion Counterpart, Biomathematics and Analysis Seminar, Vanderbilt University, Nashville, 10 February, 2005
|
Awards and Fellowships
- Royal Society Research Fellowships,UK, 1996-1997
- CNR (Italian Research Council) Visiting Professorships, Italy, 11.1998
- Alexander von Humboldt Fellowships, Germany, 1998-1999, 2003
- Max-Planck Research Fellowships, Germany, 2000-2002
| 