# Ovidiu Savin

Romanian mathematician

## Ovidiu Savin's AcademicInfluence.com Rankings

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Mathematics

## Ovidiu Savin's Degrees

- PhD Mathematics University of Bucharest
- Bachelors Mathematics University of Bucharest

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## Why Is Ovidiu Savin Influential?

(Suggest an Edit or Addition)According to Wikipedia, Ovidiu Vasile Savin is a Romanian-American mathematician who is active in the field of the partial differential equations. Scientific activity Savin received his Ph.D. in mathematics from the University of Texas at Austin in 2003 having Luis Caffarelli as advisor; he is professor of mathematics at Columbia University. Savin is mostly known for his important work on Ennio de Giorgi's conjecture about global solutions to certain semilinear equations, that he proved up to dimension 8. It is to be noticed that the conjecture turns out to be false in higher dimensions, as eventually proved by Manuel del Pino, Michał Kowalczyk, and Juncheng Wei. Savin has also worked on various regularity questions proving the gradient continuity of solutions to the infinity-Laplacian equation in two dimensions and obtaining results on the boundary regularity of solutions to the Monge–Ampère equation.

## Ovidiu Savin's Published Works

### Published Works

- Nonlocal minimal surfaces (2009) (381)
- Regularity of flat level sets in phase transitions (2009) (259)
- Local and global minimizers for a variational energy involving a fractional norm (2011) (161)
- C1 Regularity for Infinity Harmonic Functions in Two Dimensions (2005) (153)
- Γ-convergence for nonlocal phase transitions (2012) (151)
- Small Perturbation Solutions for Elliptic Equations (2007) (150)
- Regularity of nonlocal minimal cones in dimension 2 (2012) (113)
- C1,α regularity for infinity harmonic functions in two dimensions (2008) (103)
- Density estimates for a variational model driven by the Gagliardo norm (2010) (98)
- All functions are locally $s$-harmonic up to a small error (2014) (89)
- Some remarks on stability of cones for the one-phase free boundary problem (2014) (66)
- Global $W^{2,p}$ estimates for the Monge-Ampere equation (2011) (58)
- Boundary Harnack estimates in slit domains and applications to thin free boundary problems (2014) (56)
- Diffeomorphisms and Nonlinear Heat Flows (2005) (54)
- Boundary behavior of nonlocal minimal surfaces (2015) (52)
- POINTWISE C ESTIMATES AT THE BOUNDARY FOR THE MONGE-AMPÈRE EQUATION (2011) (48)
- Pointwise $C^{2,\alpha}$ estimates at the boundary for the Monge-Ampere equation (2011) (46)
- Pointwise ^{2,} estimates at the boundary for the Monge-Ampère equation (2011) (46)
- NON-LOCAL MINIMAL SURFACES (2008) (43)
- A note on interior W 2 , 1 + ε estimates for the Monge–Ampère equation (2012) (43)
- Minimizers of convex functionals arising in random surfaces (2008) (43)
- Phase Transitions, Minimal Surfaces and A Conjecture of De Giorgi (2009) (42)
- Some Singular Minimizers in Low Dimensions in the Calculus of Variations (2015) (42)
- Density Estimates for a Nonlocal Variational Model via the Sobolev Inequality (2011) (40)
- Boundary Regularity for Solutions to the Linearized Monge–Ampère Equations (2011) (39)
- A note on interior $$W^{2,1+ \varepsilon }$$estimates for the Monge–Ampère equation (2012) (38)
- Rigidity of minimizers in nonlocal phase transitions (2016) (38)
- Graph properties for nonlocal minimal surfaces (2015) (37)
- The obstacle problem for Monge Ampere equation (2005) (37)
- Some monotonicity results for minimizers in the calculus of variations (2012) (37)
- A localization theorem and boundary regularity for a class of degenerate Monge Ampere equations (2013) (37)
- Elliptic PDEs with Fibered Nonlinearities (2009) (35)
- A note on higher regularity boundary Harnack inequality (2014) (33)
- Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations (2016) (33)
- Schauder estimates for degenerate Monge–Ampère equations and smoothness of the eigenfunctions (2015) (32)
- $\Gamma$-convergence for nonlocal phase transitions (2010) (28)
- Definition of fractional Laplacian for functions with polynomial growth (2016) (28)
- A localization property at the boundary for the Monge-Ampere equation (2010) (27)
- On Monge‐Ampère equations with homogenous right‐hand sides (2007) (26)
- Regularity of Lipschitz free boundaries for the thin one-phase problem (2012) (23)
- The two membranes problem for different operators (2016) (23)
- Some minimization problems in the class of convex functions with prescribed determinant (2011) (22)
- A Nonlocal Free Boundary Problem (2014) (22)
- Minimization of a fractional perimeter-Dirichlet integral functional (2013) (22)
- C 2 , α regularity of flat free boundaries for the thin one-phase problem (2011) (20)
- Regularity of the singular set in the fully nonlinear obstacle problem (2019) (19)
- Obstacle-type problems for minimal surfaces (2016) (19)
- Rigidity of Minimizers in Nonlocal Phase Transitions II (2018) (19)
- $C^{\infty}$ regularity of certain thin free boundaries (2014) (18)
- Nonlocal Minimal Graphs in the Plane are Generically Sticky (2019) (17)
- Symmetry of global solutions to a class of fully nonlinear elliptic equations in 2D (2007) (17)
- MINIMAL SURFACES AND MINIMIZERS OF THE GINZBURG-LANDAU ENERGY (2009) (15)
- Asymptotic Behavior of Infinity Harmonic Functions Near an Isolated Singularity (2008) (14)
- A short proof of Boundary Harnack Principle (2020) (14)
- Entire solutions to a class of fully nonlinear elliptic equations (2008) (14)
- A Liouville theorem for solutions to the linearized Monge-Ampere equation (2010) (13)
- Boundary regularity for the free boundary in the one-phase problem (2017) (13)
- Almost minimizers of the one-phase free boundary problem (2019) (13)
- C1,α regularity of solutions to parabolic Monge-Ampére equations (2012) (13)
- A one-phase problem for the fractional Laplacian: regularity of flat free boundaries (2014) (12)
- Two-Phase Anisotropic Free Boundary Problems and Applications to the Bellman Equation in 2D (2016) (12)
- Boundary properties of fractional objects: Flexibility of linear equations and rigidity of minimal graphs (2019) (12)
- Some remarks on the classification of global solutions with asymptotically flat level sets (2016) (11)
- Regularity of optimal transport between planar convex domains (2018) (10)
- On boundary Hölder gradient estimates for solutions to the linearized Monge-Ampère equations (2014) (10)
- Fixed Points of Multi-valued Maps and Static Coulomb Friction Problems (2000) (10)
- A short proof of Boundary Harnack Inequality (2019) (10)
- Lipschitz regularity of solutions to two-phase free boundary problems (2017) (9)
- On the fine regularity of the singular set in the nonlinear obstacle problem (2021) (8)
- Nearby cycle sheaves for symmetric pairs (2018) (8)
- Thin one-phase almost minimizers (2018) (8)
- Contact points with integer frequencies in the thin obstacle problem (2021) (6)
- Global Solutions to Nonlinear Two‐Phase Free Boundary Problems (2017) (6)
- On Certain Degenerate One-phase Free Boundary Problems (2019) (5)
- Boundary Regularity for Solutions to the Linearized Monge–Ampère Equations (2013) (5)
- On the multiple membranes problem (2018) (5)
- A free boundary problem with optimal transportation (2004) (4)
- Half-Space Solutions with 7/2 Frequency in the Thin Obstacle Problem (2021) (4)
- On the boundary Harnack principle in Hölder domains (2020) (4)
- C^2,\alpha$ regularity of flat free boundaries for the thin one-phase problem (2011) (4)
- Viscosity solutions and the minimal surface system (2017) (4)
- Free boundary regularity in the triple membrane problem (2020) (4)
- The Alt-Phillips functional for negative powers (2022) (3)
- Regularity results for the equation $u_{11}u_{22} = 1$. (2018) (3)
- Boundary regularity for Monge-Ampère equations with unbounded right hand side (2018) (2)
- Symmetry of entire solutions for a class of semilinear elliptic equations (2006) (2)
- Quasi-Harnack inequality (2018) (2)
- On divergent fractional Laplace equations (2019) (2)
- On the Regularity of Optimal Transports Between Degenerate Densities (2021) (2)
- Global C2,α estimates for the Monge-Ampère equation on polygonal domains in the plane (2023) (1)
- Global W2,1+ estimates for Monge-Ampère equation with natural boundary condition (2020) (1)
- Boundary Hölder Gradient Estimates for the Monge–Ampère Equation (2020) (1)
- Compactness estimates for minimizers of the Alt-Phillips functional of negative exponents (2022) (1)
- Boundary H\"older gradient estimates for the Monge-Amp\`ere equation (2018) (0)
- Perturbative estimates for the one-phase Stefan problem (2020) (0)
- Global $W^{2,1+\varepsilon}$ estimates for Monge-Amp\`ere equation with natural boundary condition (2018) (0)
- Schauder estimates for degenerate Monge–Ampère equations and smoothness of the eigenfunctions (2016) (0)
- Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations (2018) (0)
- Regularity of nonlocal minimal cones in dimension 2 (2012) (0)
- Boundary Hölder Gradient Estimates for the Monge–Ampère Equation (2020) (0)
- Regularity results for the equation \begin{document}$ u_{11}u_{22} = 1 $\end{document} (2019) (0)
- On the Parabolic Boundary Harnack Principle (2021) (0)
- $C^{1,\al}$ regularity of solutions to parabolic Monge-Amp\'ere equations (2009) (0)
- Nonlocal Minimal Graphs in the Plane are Generically Sticky (2020) (0)
- Some remarks on stability of cones for the one-phase free boundary problem (2015) (0)
- Some remarks on the classification of global solutions with asymptotically flat level sets (2017) (0)
- Non $C^1$ solutions to the special Lagrangian equation (2023) (0)
- Local and global minimizers for a variational energy involving a fractional norm (2012) (0)
- Two-Phase Anisotropic Free Boundary Problems and Applications to the Bellman Equation in 2D (2017) (0)
- Some Singular Minimizers in Low Dimensions in the Calculus of Variations (2016) (0)
- An energy model for harmonic functions with junctions (2023) (0)
- On boundary H\"older gradient estimates for solutions to the linearized Monge-Amp\`ere equations (2013) (0)
- Free boundary regularity in the multiple membrane problem in the plane (2021) (0)
- Global $C^{2,\alpha}$ estimates for the Monge-Ampère equation on polygonal domains in the plane (2019) (0)
- Graph properties for nonlocal minimal surfaces (2016) (0)

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