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Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2017, Volume 56, Issue 5
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 04/2018, Volume 43, Issue 4, pp. 616 - 627
We consider the problem of constrained Ginibre ensemble with prescribed portion of eigenvalues on a given curve Γ⊂ℝ 2 and relate it to a thin obstacle problem.... 
thin obstacle | global regularity | Free boundary | obstacle problem | Primary: 35R35 | MATHEMATICS | MATHEMATICS, APPLIED | Eigenvalues
Journal Article
Analysis, ISSN 0174-4747, 01/2019, Volume 38, Issue 4, pp. 155 - 165
We consider an overdetermined problem associated to an inhomogeneous infinity-Laplace equation. More precisely, the domain of the problem is required to... 
35N25 | Infinity-Laplacian | 35R35 | overdetermined problems | viscosity solutions
Journal Article
Inverse Problems and Imaging, ISSN 1930-8337, 2019, Volume 13, Issue 2, pp. 377 - 400
We consider an inverse obstacle problem for the acoustic transient wave equation. More precisely, we wish to reconstruct an obstacle characterized by a... 
Wave equation | Lateral cauchy data | Nverse obstacle problem | Unique continuation | Level set method | Quasi-reversibility | lateral Cauchy data | MATHEMATICS, APPLIED | quasi-reversibility | unique continuation | wave equation | level set method | SOLVE | PHYSICS, MATHEMATICAL | Inverse obstacle problem | SCATTERING | EXTERIOR APPROACH
Journal Article
Mathematische Annalen, ISSN 0025-5831, 6/2013, Volume 356, Issue 2, pp. 737 - 792
The two-phase free boundary value problem for the isothermal Navier–Stokes system is studied for general bounded geometries in absence of phase transitions,... 
Mathematics, general | Mathematics | 35R35 | 35Q30 | 76T10 | 76D45 | EXISTENCE | FLUIDS | MATHEMATICS | EVOLUTION-EQUATIONS | SPACES
Journal Article
Mathematische Annalen, ISSN 0025-5831, 8/2018, Volume 371, Issue 3, pp. 1683 - 1735
We study the obstacle problem for the fractional Laplacian with drift, $$\min \{(-\varDelta )^su + b \cdot \nabla u,\,u -\varphi \} = 0$$... 
35B65 | Mathematics, general | Mathematics | 35R35 | 47G20 | MATHEMATICS | EQUATIONS | FREE-BOUNDARY | HIGHER REGULARITY | OPERATORS
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 9/2017, Volume 29, Issue 3, pp. 957 - 979
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 03/2013, Volume 162, Issue 4, pp. 627 - 642
The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice Z(d), in which sites with at... 
MATHEMATICS | 60K35 | 35R35
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 11/2015, Volume 218, Issue 2, pp. 647 - 697
For a class of systems of semi-linear elliptic equations, including for p = 2 (variational-type interaction) or p = 1 (symmetric-type interaction), we prove... 
MATHEMATICS, APPLIED | MODELING PHASE-SEPARATION | MECHANICS | FREE-BOUNDARIES | SPATIAL SEGREGATION | THEOREMS | EQUATIONS | MONOTONICITY | BOSE-EINSTEIN CONDENSATION | ELLIPTIC SYSTEM | DIFFUSION-SYSTEMS | CONJECTURE | Mathematics - Analysis of PDEs
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 9/2014, Volume 26, Issue 3, pp. 655 - 672
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 07/2018, Volume 43, Issue 7, pp. 1073 - 1101
We continue the analysis of the two-phase free boundary problems initiated by ourselves, studying where we studied the linear growth of minimizers in a... 
monotonicity formula | p-Laplace | Two phase | free boundary regularit | Primary: 35R35 | MATHEMATICS | FLAT FREE-BOUNDARIES | MATHEMATICS, APPLIED | LIPSCHITZ REGULARITY | EQUATIONS | MINIMUM PROBLEM | DOMAINS | Free boundaries
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 5/2019, Volume 109, Issue 5, pp. 1145 - 1166
This paper investigates an anisotropic diffusion equation with degeneracy on the boundary. A new kind of weak solution is introduced, and the existence of the... 
Geometry | 35L85 | Stability | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | 35R35 | Anisotropic diffusion equation | Physics | Boundary value condition | 35L65 | PHYSICS, MATHEMATICAL | Anisotropy
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 5/2016, Volume 343, Issue 3, pp. 1039 - 1113
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid... 
Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | Mathematics - Analysis of PDEs
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 14
Consider a nonlinear diffusion equation related to the p-Laplacian. Different from the usual evolutionary p-Laplacian equation, the equation is degenerate on... 
35L85 | p -Laplacian | uniqueness | Analysis | Mathematics, general | Mathematics | 35R35 | Applications of Mathematics | boundary value condition | 35L65 | diffusion coefficient | p-Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | Laplace equation | Diffusion | Diffusion coefficient | Uniqueness | Research
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 4/2016, Volume 67, Issue 2, pp. 1 - 11
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 07/2018, Volume 167, Issue 10, pp. 1825 - 1882
We study the minimum problem for the functional integral(Omega)(vertical bar del u vertical bar(2) + Q(2) chi({vertical bar u vertical bar>0}))dx with the... 
MATHEMATICS | REGULARITY | HARMONIC-FUNCTIONS | Mathematics - Analysis of PDEs
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 12/2012, Volume 24, Issue 4, pp. 873 - 895
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 4/2016, Volume 204, Issue 1, pp. 1 - 82
We will show optimal regularity for minimizers of the Signorini problem for the Lame system. In particular if $$\mathbf{u }=(u^1,u^2,\dots ,u^n)\in... 
Mathematics, general | Mathematics | Secondary 35B40 | 35J60 | Primary 35R35 | MATHEMATICS | Maximum principle | Partial differential equations | Mathematical analysis | Regularity | Free boundaries | Texts | Scalars | Graphs | Optimization
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 6/2019, Volume 58, Issue 3, pp. 1 - 19
In this paper, we prove a local $$C^{1}$$ C1 -regularity of the free boundary for the (hybrid) double obstacle problem with an upper obstacle $$\psi $$ ψ ,... 
Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Regularity of free boundary | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 35R35 | Free boundary problem | Obstacle problem | MATHEMATICS | MATHEMATICS, APPLIED | FREE-BOUNDARY
Journal Article
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