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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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A Priori and a Posteriori Error Analysis for Generic Linear Elliptic Problems

Tikrit Journal of Pure Science, 2022
In this paper, a priori error analysis has been examined for the continuous Galerkin finite element method which is used for solving a generic scalar and a generic system of linear elliptic equations.
Hala Raad, Mohammad Sabawi
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Strongly Elliptic Differential-Difference Equations with Mixed Boundary Conditions in a Cylindric Domain

Современная математика: Фундаментальные направления, 2019
We consider strongly elliptic differential-difference equations with mixed boundary conditions in a cylindrical domain. We establish the connection between such problems and nonlocal mixed problems for strongly elliptic differential equations, and prove ...
V. V. Liiko, A. L. Skubachevskii
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Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains

Boundary Value Problems, 2006
We establish the global Hölder estimates for solutions to second-order elliptic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded.
Sungwon Cho, Mikhail Safonov
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Compactness methods for Hölder estimates of certain degenerate elliptic equations

Electronic Journal of Qualitative Theory of Differential Equations, 2012
In this paper we obtain the interior $C^{1,\alpha}$ regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local $L^\infty$ estimates and weak Harnack inequality for second-order linear elliptic equations,
Fengping Yao, Mijia Lai, Huilian Jia
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Picone-type inequalities for nonlinear elliptic equations with first-order terms and their applications

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, Yoshida Norio, Jaroš Jaroslav   +2 more
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$C^{1,\alpha}$ regularity for elliptic equations with the general nonstandard growth conditions [PDF]

Mathematica Bohemica
We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on $\Omega$. We prove the global $C^{1, \alpha}$ regularity of bounded weak solutions of these equations with the Dirichlet boundary ...
Sungchol Kim, Dukman Ri
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Picone-type inequalities for nonlinear elliptic equations and their applications

Journal of Inequalities and Applications, 2001
Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are ...
Takaŝi Kusano, Yoshida Norio, Jaroš Jaroslav   +2 more
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Elliptic triad

Physics Letters B
The triad refers to embedding the Macdonald polynomials into the Noumi-Shiraishi functions and their reduction to solutions of simple linear equations at particular values of t. It provides an alternative definition of Macdonald theory.
A. Mironov, A. Morozov, A. Popolitov, Z. Zakirova   +3 more
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Sturm comparison theorems for some elliptic type equations via Picone-tpye inequalities

Electronic Journal of Qualitative Theory of Differential Equations, 2016
Sturm theorems have appeared as one of the fundamental subjects in qualitative theory to determine properties of the solutions of differential equations. Motivated by some recent developments for half-linear type elliptic equations, we obtain Picone-type
Aydin Tiryaki, Sinem Sahiner, Emine Misirli   +2 more
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