A deterministic-control-based approach to motion by curvature (Viscosity Solution Theory of Differential Equations and its Developments)

By Robert V. Kohn, Sylvia Serfaty. 2005

135 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/fe9b766173efa99aa32600d54571d653035e563a

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Citations in the corpus

On the definition and properties of p-harmonious functions (2012, background): “For a deterministic-control-based approach see [9] and [10].”
Nonlocal Tug‐of‐War and the Infinity Fractional Laplacian (2010, background): “see [6] and the references therein). There are many variations on the rules of the game, for example adding a running cost of movement, which give rise to a class of related “Aronsson equations”, see [1, 11, 12]. In this paper we consider a variation of the game where, instead of ﬂipping a coin, at ”
A mixed problem for the infinity Laplacian via Tug-of-War games (2007, methodology): “ II is trying to minimize Player I’s outcome (or, since the game is zero-sum, to maximize his own outcome). Recently, these type of games have been used in connection with some PDE problems, see [6], [15], [18], [19]. For the reader’s convenience, let us ﬁrst describe brieﬂy the game introduced in [”
Very singular diffusion equations: second and fourth order problems (2010, background): “It is interesting to study recent differential game approximation by Kohn and Serfaty [ 79 ,80] of a solution although approximation scheme for singular interfacial energy is not yet given.”
Tug-of-war with noise: A game-theoretic view of the $p$-Laplacian (2006, background): “the same as in the random turn case. 3.2 Direction selection and Spencer’s game The following game (along with other variants) was introduced by Spencer [16] and studied in detail by Kohn and Serfaty [8]. We focus on the case d= 2, although many natural variants exist in higher dimensions. Fix Ω,x,F”
A deterministic‐control‐based approach to fully nonlinear parabolic and elliptic equations (2010, methodology): “work [35], which gave deterministic game interpretations for a variety of geometric evolution laws including motion by curvature.”