Symmetries, Reductions and Exact Solutions of Nonstationary Monge–Ampère Type Equations
MathematicsA family of strongly nonlinear nonstationary equations of mathematical physics with three independent variables is investigated, which contain an arbitrary degree of the first derivative with respect to time and a quadratic combination of second ...
Alexander V. Aksenov, Andrei D. Polyanin
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The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures. [PDF]
Calc Var Partial Differ Equ, 2022 Colesanti A, Ludwig M, Mussnig F.
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Extended symmetry of the Witten-Dijkgraaf-Verlinde-Verlinde equation of Monge-Ampere type [PDF]
Opuscula MathematicaWe construct the Lie algebra of extended symmetry group for the Monge-Ampere type Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation. This algebra includes novel generators that are unobtainable within the framework of the classical Lie approach and ...
Patryk Sitko, Ivan Tsyfra
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Positive Solutions of Two-Point Boundary Value Problems for Monge-Ampère Equations
Journal of Function Spaces, 2015 This paper considers the following boundary value problem: ((-u'(t))n)'=ntn-1f(u(t ...
Baoqiang Yan, Meng Zhang
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Local Regularity of the Complex Monge-Ampere Equation
, 2013 In this thesis, we present a self-contained account of the current development in the local regularity theory of the complex Monge-Ampere equation through the modern fully-nonlinear PDE point of view. We have apply the modern elliptic techniques to establish new local regularity results.
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A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds
Journal of Applied Mathematics, 2013 We study the asymptotic behavior of the parabolic Monge-Ampère equation in , in , where is a compact complete Riemannian manifold, λ is a positive real parameter, and is a smooth function.
Qiang Ru
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A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation. [PDF]
J Sci Comput, 2022 Caboussat A +2 more
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Contact Geometry of Hyperbolic Equations of Generic Type
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6), Goursat (class 6-7) and generic (class 7-7 ...
Dennis The
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The Föppl-von Kármán equations of elastic plates with initial stress. [PDF]
R Soc Open Sci, 2022 Ciarletta P, Pozzi G, Riccobelli D.
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Spline element method for the Monge-Ampere equation
, 2010 We analyze the convergence of an iterative method for solving the nonlinear system resulting from a natural discretization of the Monge-Ampère equation with $C^1$ conforming approximations. We make the assumption, supported by numerical experiments for the two dimensional problem, that the discrete problem has a convex solution.
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