Free boundary regularity for fully nonlinear non-homogeneous two-phase problems [PDF]
, 2013 Daniela De Silva +2 more
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Free boundary problems with nonlocal and local diffusions Ⅱ: Spreading-vanishing and long-time behavior [PDF]
Discrete & Continuous Dynamical Systems - B, 2019 This is part II of our study on the free boundary problems with nonlocal and local diffusions. In part I, we obtained the existence, uniqueness, regularity and estimates of global solution.
Jianping Wang, Mingxin Wang
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Free boundary problems in the spirit of Sakai’s theorem
Comptes Rendus. Mathématique, 2022 A Schwarz function on an open domain $\Omega $ is a holomorphic function satisfying $S(\zeta )=\bar{\zeta }$ on $\Gamma $, which is part of the boundary of $\Omega $.
Vardakis, Dimitris, Volberg, Alexander
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Hyperbolic free boundary problems and applications to wave-structure interactions [PDF]
Indiana University Mathematics Journal, 2018 Motivated by a new kind of initial boundary value problem (IBVP) with a free boundary arising in wave-structure interaction, we propose here a general approach to one-dimensional IBVP as well as transmission problems.
T. Iguchi, D. Lannes
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Branch points for (almost-)minimizers of two-phase free boundary problems
Forum of Mathematics, Sigma, 2023 We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family of minimizers to an Alt–Caffarelli–Friedman-type functional whose free boundaries contain branch points in the strict ...
Guy David +3 more
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On Certain Degenerate One-phase Free Boundary Problems [PDF]
SIAM Journal on Mathematical Analysis, 2019 We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more generally for ...
D. Silva, O. Savin
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From individual-based mechanical models of multicellular systems to free-boundary problems [PDF]
Interfaces and free boundaries (Print), 2019 In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteristics.
T. Lorenzi, P. Murray, M. Ptashnyk
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Regularity results for a penalized boundary obstacle problem
Mathematics in Engineering, 2021 In this paper we are concerned with a two-penalty boundary obstacle problem of interest in thermics, fluid dynamics and electricity. Specifically, we prove existence, uniqueness and optimal regularity of the solutions, and we establish structural ...
Donatella Danielli, Rohit Jain
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Properties of the free boundary near the fixed boundary of the double obstacle problems
Bulletin of Mathematical Sciences, 2022 In this paper, we study the tangential touch and [Formula: see text] regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator.
Jinwan Park
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Quantitative stratification for some free-boundary problems [PDF]
Transactions of the American Mathematical Society, 2017 In this paper we prove the rectifiability of and measure bounds on the singular set of the free boundary for minimizers of a functional first considered by Alt-Caffarelli.
Nick Edelen, Max Engelstein
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