A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales [PDF]
Communications in Computational Physics, 2020 Algorithms based on deep neural networks (DNNs) have attracted increasing attention from the scientific computing community. DNN based algorithms are easy to implement, natural for nonlinear problems, and have shown great potential to overcome the curse ...
Xi-An Li, Zhi-Qin John Xu, Lei Zhang
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Regularity for solutions of fully nonlinear elliptic equations with nonhomogeneous degeneracy [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2019 We prove that viscosity solutions to fully nonlinear elliptic equations with degeneracy of double phase type are locally C1, γ-regular.
C. Filippis
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Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions [PDF]
Archive for Rational Mechanics and Analysis, 2017 In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we derive the pointwise Cα, C1,α and C2,α regularity. As byproducts, we also
Dongsheng Li, Kai Zhang
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Fractional Differentiability for Solutions of Nonlinear Elliptic Equations [PDF]
Potential Analysis, 2016 We study nonlinear elliptic equations in divergence form divA(x,Du)=divG.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
A. L. Bais'on +4 more
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Some remarks on singular solutions of nonlinear elliptic equations. I [PDF]
, 2009 The paper concerns singular solutions of nonlinear elliptic ...
Caffarelli, Luis +2 more
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Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations.
Bica Ion, Mucalica Ana
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On strong comparison principle for semicontinuous viscosity solutions of some nonlinear elliptic equations [PDF]
, 2005 The strong comparison principle for semicontinuous viscosity solutions of some nonlinear elliptic equations are considered. For linear elliptic equations it is well known that the strong comparison principle is equivalent to the strong maximum ...
Giga, Yoshikazu, Ohnuma, Masaki
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Linear Superposition in Nonlinear Equations [PDF]
, 2001 Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a large class of additional solutions.
A. C. Newell +13 more
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Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Journal of Applied Mathematics, 2012 We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method.
Khaled A. Gepreel, A. R. Shehata
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Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations
Моделирование и анализ информационных систем, 2014 The problem of constructing and classifying elliptic solutions of nonlinear differential equations is studied. An effective method enabling one to find an elliptic solution of an autonomous nonlinear ordinary differential equation is described.
M. V. Demina, N. A. Kudryashov
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