Michael Goldman go back to home page
Papers and Reports
- A gradient flow approach to relaxation rates for the multi-dimensional Cahn-Hilliard equation , with with L. De Luca and M. Strani, submitted, pdf.
- Quantitative estimates for bending energies and applications to non-local variational problems , with with M. Novaga and M. Röger, submitted, pdf.
- A Ginzburg-Landau model with topologically induced free discontinuities , with B. Merlet and V. Millot, submitted, pdf.
- Self-similar minimizers of a branched transport functional , submitted, pdf.
- A variational proof of partial regularity for optimal transportation maps , with F. Otto, submitted, pdf.
For a simplified version in the case of constant densities see below.
- On the optimality of stripes in a variational model with non-local interactions , with E. Runa, submitted, pdf.
- A branched transport limit of the Ginzburg-Landau functional , with S. Conti, F. Otto and S. Serfaty, accepted in J. Ecole Polytechnique , pdf.
- On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint , with M. Novaga and B. Ruffini, accepted in Analysis and PDEs, pdf.
- Phase segregation for binary mixtures of Bose-Einstein Condensates , with B. Merlet, accepted in SIAM J. Math. Analysis , pdf.
- New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky equations , with M. Josien and F. Otto, accepted in CPDE , pdf.
- Study of island formation in epitaxially strained films on unbounded domains , with P. Bella and B. Zwicknagl , ARMA, 218, 2015, no. 1, 163--217 , pdf.
- Existence and stability for a non-local isoperimetric model of charged liquid drops , with M. Novaga and B. Ruffini, ARMA, 217, 2015, no. 1, 1--36 , pdf.
- Sharp interface limit for two components Bose-Einstein condensates , with J. Royo-Letelier , accepted in ESAIM COCV, pdf.
- Nucleation barriers at corners for a cubic-to-tetragonal phase transformation , with P. Bella , Proc. Roy. Soc. Edimburgh, 145 A, 2015, 715-724, , pdf.
- Fine properties of the subdifferential for a class of one-homogeneous functionals, with A. Chambolle and M. Novaga , Adv. Calc. Var., vol. 8 n. 1, 31-42, 2015 , pdf.
- Scaling law and reduced models for epitaxially strained films, with B. Zwicknagl , SIAM J. Math. Analysis, 46 no. 1, 1--24, 2015 , pdf.
- The Gamma-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension, with G. Bellettini and A. Chambolle , M3AS, vol. 24, Issue 6, 2014., pdf.
- Plane-like minimizers and differentiability of the stable norm, with A. Chambolle and M. Novaga , accepted in J. Geometric Analysis, pdf.
- Representation, relaxation and convexity for variational problems in Wiener spaces, with A. Chambolle and M. Novaga , J. Math. Pures Appl, 99, 2013, 419-435, pdf.
- Approximation and relaxation of perimeter in the Wiener space, with M. Novaga , Annales IHP - Analyse Non linéaire, vol. 29, 2012, 525-544, pdf.
- A geometric approach for convexity in some variational problem in the Gauss space , Rendiconti di Padova, vol. 129, 2013, pdf.
- Volume-constrained minimizers for the prescribed curvature problem in periodic media, with M. Novaga , Calc. Var. and PDE, vol. 44, Issue 3, 2012, 297-318, pdf.
- Continuous Primal-Dual Methods for Image Processing, SIAM Journal of Imaging Sciences, vol. 4, no. 1, 2011, pdf.
- Equilibrium shapes of charged droplets and related problems: (mostly) a review , with B. Ruffini , accepted for Geometric flows, pdf.
- Existence and qualitative properties of isoperimetric sets in periodic media, with A. Chambolle and M. Novaga, "Geometric Partial Differential Equations", Edizioni della Normale, CRM Series, vol. 15, pp. 93-104, 2013, pdf.
- A variational proof of partial regularity for optimal transportation maps between sets , with F. Otto, pdf.
This is a simplified version of the paper "A variational proof of partial regularity for optimal transportation maps".
Thesis and Reports
- Quelques applications des fonctions a variation bornee en dimension finie et infinie, 2011, PhD Thesis (advisor A. Chambolle, CMAP), pdf.
- Etude d'une methode de recherche de points selle pour certains problemes de reconstruction d'image, 2009, master thesis (advisor A. Chambolle, CMAP), pdf.
- Introduction to the Study of the Signature Function, 2007, thesis ending the first year of master studies (advisor S. Esedoglu, Univ. of Michigan), pdf.
- Minimisation singuliere pour la restauration d'images, 2006, undergraduate thesis (advisor A. Chambolle, CMAP), pdf.