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New Trends in Free Boundary Problems [PDF]
Advanced Nonlinear Studies, 2017 We present a series of recent results on some new classes of free boundary problems.Differently from the classical literature, the problems considered have either a “nonlocal” feature (e.g., the interaction or/and the interfacial energy may depend on ...
Dipierro Serena +2 more
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Optimal approximations for the free boundary problems of the space-time fractional Black-Scholes equations using a combined physics-informed neural network [PDF]
Scientific ReportsThe combined physics-informed neural network is employed to deal with the free boundary problems of fractional Black-Scholes equations. The solution assumption and the loss function are determined, the transfer learning is borrowed, the combined neural ...
Lina Song +4 more
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An overview of unconstrained free boundary problems [PDF]
Philosophical Transactions Series A, Mathematical, Physical, and Engineering Sciences, 2015 Henrik Shahgholian, Alessio Figalli
exaly +2 more sources
Multidimensional transonic shock waves and free boundary problems
Bulletin of Mathematical Sciences, 2022 We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics.
Gui-Qiang G. Chen, Mikhail Feldman
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A Nonlocal Free Boundary Problem [PDF]
SIAM Journal on Mathematical Analysis, 2015 Given~$s,σ\in(0,1)$ and a bounded domain~$Ω\subset\R^n$, we consider the following minimization problem of $s$-Dirichlet plus $σ$-perimeter type $$ [u]_{ H^s(\R^{2n}\setminus(Ω^c)^2) } + \Per_σ\left(\{u>0\},Ω\right), $$ where~$[ \cdot]_{H^s}$ is the fractional Gagliardo seminorm and $\Per_σ$ is the fractional perimeter. Among other results, we prove
S. Dipierro, O. Savin, E. Valdinoci
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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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ON BERNOULLI'S FREE BOUNDARY PROBLEM WITH A RANDOM BOUNDARY [PDF]
International Journal for Uncertainty Quantification, 2017 This article is dedicated to the solution of Bernoulli’s exterior free boundary problem in the situation of a random interior boundary. We provide the theoretical background that ensures the well-posedness of the problem under consideration and describe two different frameworks to define the expectation and the deviation of the resulting annular domain.
Dambrine, Marc +3 more
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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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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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Free boundaries in problems with hysteresis [PDF]
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015 Here, we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes ‘with memory’ in which various substances interact according to hysteresis law.
D. E. Apushkinskaya, N. N. Uraltseva
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