Picone-type inequalities for nonlinear elliptic equations with first-order terms and their applications [PDF]
Journal of Inequalities and Applications, 2006 Picone-type inequalities are established for nonlinear elliptic equations which are generalizations of nonself-adjoint linear elliptic equations, and Sturmian comparison theorems are derived as applications.
Takaŝi Kusano +2 more
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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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On the numerical solution of some differential equations with nonlocal integral boundary conditions via Haar wavelet [PDF]
Proceedings of the Estonian Academy of Sciences, 2022 Differential equations with nonlocal boundary conditions are used to model a number of physical phenomena encountered in situations where data on the boundary cannot be measured directly. This study explores numerical solutions to elliptic, parabolic and
Imran Aziz +2 more
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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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Nonlinear elliptic differential equations with multivalued nonlinearities [PDF]
Proceedings Mathematical Sciences, 2001 In this work, certain quasilinear elliptic boundary value problems are investigated. Homogeneous Dirichlet boundary condition is always considered. In the first result, assuming that the multivalued monotone nonlinearity \(\beta\) satisfies \(\operatorname {dom}\beta = R\) and the existence of an upper and a lower solution, the existence of a solution ...
Fiacca A +3 more
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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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Open Physics, 2021 This research paper uses a direct algebraic computational scheme to construct the Jacobi elliptic solutions based on the conformal fractional derivatives for nonlinear partial fractional differential equations (NPFDEs). Three vital models in mathematical
Gepreel Khaled A., Mahdy Amr M. S.
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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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Existence and uniqueness results for possibly singular nonlinear elliptic equations with measure data [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2017 We study existence and uniqueness of solutions to a nonlinear elliptic boundary value problem with a general, and possibly singular, lower order term, whose model is -Δpu=H(u)μinΩ,u>0inΩ,u=0on∂Ω.\documentclass[12pt]{minimal} \usepackage{amsmath ...
Linda Maria De Cave +2 more
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A spectral method for nonlinear elliptic equations [PDF]
Numerical Algorithms, 2016 26 pages.
Atkinson, Kendall +2 more
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