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Original Articles

Anisotropic variable exponent Sobolev spaces and -Laplacian equations

Pages 623-642 | Received 04 Jan 2010, Accepted 30 Jan 2010, Published online: 11 Jun 2010

Keep up to date with the latest research on this topic with citation updates for this article.

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Nour Elhouda Allaoui & Fares Mokhtari. (2023) Anisotropic elliptic system with variable exponents and degenerate coercivity with L data. Applicable Analysis 0:0, pages 1-21.
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A. Razani & T. Soltani. (2023) Solutions of an anisotropic elliptic problem involving nonlinear terms. Quaestiones Mathematicae 0:0, pages 1-20.
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Mohammed Massar. (2022) Existence results for an anisotropic variable exponent Kirchhoff-type problem. Complex Variables and Elliptic Equations 0:0, pages 1-18.
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Hocine Ayadi & Fares Mokhtari. (2020) Entropy solutions for nonlinear anisotropic elliptic equations with variable exponents and degenerate coercivity. Complex Variables and Elliptic Equations 65:5, pages 717-739.
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L. M. Kozhevnikova. (2020) On solutions of anisotropic elliptic equations with variable exponent and measure data. Complex Variables and Elliptic Equations 65:3, pages 333-367.
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S. Khademloo, G. A. Afrouzi & T. Norouzi Ghara. (2018) Infinitely many solutions for anisotropic variable exponent problems. Complex Variables and Elliptic Equations 63:9, pages 1353-1369.
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Maria-Magdalena Boureanu. (2023) Multiple solutions for two general classes of anisotropic systems with variable exponents. Journal d'Analyse Mathématique.
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Ahmed Ahmed & Mohamed Saad Bouh Elemine Vall. (2023) Minimization of elliptic non-local functionals involving $$\vec {p}(\cdot )$$-Laplacian. Journal of Elliptic and Parabolic Equations 9:1, pages 331-354.
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Ibrahime Konaté & Arouna Ouédraogo. (2023) Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and -Data . International Journal of Differential Equations 2023, pages 1-11.
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Mokhtar Naceri. (2023) Anisotropic nonlinear weighted elliptic equations with variable exponents. Georgian Mathematical Journal 30:2, pages 277-285.
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Cholmin Sin. (2023) -regularity for steady flows of electrorheological fluids in 2D . Nonlinear Analysis 229, pages 113223.
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Rakesh Arora & Sergey Shmarev. (2023) Existence and global second-order regularity for anisotropic parabolic equations with variable growth. Journal of Differential Equations 349, pages 83-124.
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Barbara Brandolini & Florica C. Cîrstea. (2023) Anisotropic elliptic equations with gradient-dependent lower order terms and $ L^1 $ data. Mathematics in Engineering 5:4, pages 1-33.
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Leandro Tavares. (2023) Solutions for a class of problems driven by an anisotropic $ (p, q) $-Laplacian type operator. Communications in Analysis and Mechanics 15:3, pages 533-550.
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Mohamed Badr Benboubker, Hayat Benkhalou & Hassane Hjiaj. (2022) Weak and renormalized solutions for anisotropic Neumann problems with degenerate coercivity. Boletim da Sociedade Paranaense de Matemática 41, pages 1-25.
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G A Afrouzi, S Khademloo, L Li & Ghara T Norouzi. (2022) Nontrivial solution for an anisotropic variable exponent problem with Neumann boundary condition. Proceedings - Mathematical Sciences 132:2.
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Leandro S. Tavares. (2022) Multiple solutions for a system involving an anisotropic variable exponent operator. Boundary Value Problems 2022:1.
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Leandro S. Tavares. (2022) Multiplicity of solutions for an anisotropic variable exponent problem. Boundary Value Problems 2022:1.
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Noureddine Dechoucha, Fares Mokhtari & Hocine Ayadi. (2022) Anisotropic degenerate elliptic problems in $${\mathbb {R}}^N$$ with variable exponent and locally integrable data. Journal of Elliptic and Parabolic Equations 8:2, pages 939-957.
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Hellal Abdelaziz & Fares Mokhtari. (2022) Nonlinear anisotropic degenerate parabolic equations with variable exponents and irregular data. Journal of Elliptic and Parabolic Equations 8:1, pages 513-532.
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Naceri Mokhtar & Mohamed Badr Benboubker. (2022) Distributional solutions of anisotropic nonlinear elliptic systems with variable exponents: existence and regularity. Advances in Operator Theory 7:2.
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El Amrouss Abdelrachid & Ali El Mahraoui. (2022) Existence and multiplicity of solutions for anisotropic elliptic equation. Boletim da Sociedade Paranaense de Matemática 40, pages 1-12.
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Rabah Mecheter. (2022) Anisotropic parabolic problem with variable exponent and regular data. Mathematical Modeling and Computing 9:3, pages 519-535.
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Cholmin Sin. (2021) The Existence of Strong Solution for Generalized Navier-Stokes Equations with -Power Law under Dirichlet Boundary Conditions . Advances in Mathematical Physics 2021, pages 1-11.
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Ahmed Aberqi, Benali Aharrouch & Jaouad Bennouna. (2021) On Some $\protect \overrightarrow {p(x)}$ Anisotropic Elliptic Equations in Unbounded Domain. Acta Mathematica Vietnamica 46:4, pages 701-718.
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V. F. Vildanova & F. Kh. Mukminov. (2021) Existence of Weak Solutions of Aggregation Integro-Differential Equations. Journal of Mathematical Sciences 259:6, pages 775-790.
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L. M. Kozhevnikova & A. Sh. Kamaletdinov. (2021) Existence of Solutions of Anisotropic Elliptic Equations with Variable Indices of Nonlinearity in ℝn. Journal of Mathematical Sciences 257:1, pages 48-60.
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Anass Ourraoui & Maria Alessandra Ragusa. (2021) An Existence Result for a Class of p(x)—Anisotropic Type Equations. Symmetry 13:4, pages 633.
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Ahmed Youssfi & Mohamed Mahmoud Ould Khatri. (2021) Continuous imbedding in Musielak spaces with an application to anisotropic nonlinear Neumann problems. Electronic Journal of Differential Equations 2021:01-104, pages 26.
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L. M. Kozhevnikova. (2021) On Entropy Solutions of Anisotropic Elliptic Equations with Variable Nonlinearity Indices in Unbounded Domains. Journal of Mathematical Sciences 253:5, pages 692-709.
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F. Kh. Mukminov. (2020) Existence and Uniqueness of Renormalized Solutions to Parabolic Problems for Equations with Diffuse Measure. Journal of Mathematical Sciences 247:6, pages 900-925.
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L. M. Kozhevnikova. (2020) Equivalence of Entropy and Renormalized Solutions of Anisotropic Elliptic Problem in Unbounded Domains with Measure Data. Russian Mathematics 64:1, pages 25-39.
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Ahmed Ahmed & Mohamed Saad Bouh Elemine Vall. (2020) Three weak solutions for a Neumann elliptic equations involving the p→(x) \vec p\left( x \right) -Laplacian operator. Nonautonomous Dynamical Systems 7:1, pages 224-236.
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Martin Bohner, Giuseppe Caristi, Fariba Gharehgazlouei & Shapour Heidarkhani. (2020) Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian. Nonautonomous Dynamical Systems 7:1, pages 53-64.
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Ibrahime Konaté & Stanislas Ouaro. (2019) Multivalued anisotropic problem with Fourier boundary condition involving diffuse Radon measure data and variable exponents. Glasnik Matematicki 54:1, pages 211-232.
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Fares Mokhtari & Rabah Mecheter. (2019) Anisotropic Degenerate Parabolic Problems in $$\mathbb {R}^N$$ R N with Variable Exponent and Locally Integrable Data. Mediterranean Journal of Mathematics 16:3.
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L. M. Kozhevnikova. (2019) Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents. Sbornik: Mathematics 210:3, pages 417-446.
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Лариса Михайловна Кожевникова & Larisa Mikhailovna Kozhevnikova. (2019) Энтропийные и ренормализованные решения анизотропных эллиптических уравнений с переменными показателями нелинейностейEntropy and renormalized solutions of anisotropic elliptic equations with variable exponents of nonlinearities. Математический сборник Matematicheskii Sbornik 210:3, pages 131-161.
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Said Taarabti, Zakaria El Allali & Khalil Ben Haddouch. On an eigenvalue problem for an anisotropic elliptic equation. On an eigenvalue problem for an anisotropic elliptic equation.
Cholmin Sin. (2018) Global regularity of weak solutions for steady motions of electrorheological fluids in 3D smooth domain. Journal of Mathematical Analysis and Applications 461:1, pages 752-776.
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A. Sh. Kamaletdinov, L. M. Kozhevnikova & L. Yu. Melnik. (2018) Existence of Solutions of Anisotropic Elliptic Equations with Variable Exponents in Unbounded Domains. Lobachevskii Journal of Mathematics 39:2, pages 224-235.
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Cholmin Sin. (2017) The existence of strong solutions to steady motion of electrorheological fluids in 3D cubic domain. Journal of Mathematical Analysis and Applications 445:1, pages 1025-1046.
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Mei Yu, Li Wang & Sufang Tang. (2016) Existence of solutions for an anisotropic elliptic problem with variable exponent and singularity. Mathematical Methods in the Applied Sciences 39:10, pages 2761-2767.
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Idrissa Ibrango & Stanislas Ouaro. (2016) ENTROPY SOLUTIONS FOR NONLINEAR ELLIPTIC ANISOTROPIC PROBLEMS WITH HOMOGENEOUS NEUMANN BOUNDARY CONDITION. Journal of Applied Analysis & Computation 6:2, pages 271-292.
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Maria-Magdalena Boureanu & Cristian Udrea. (2015) No--flux boundary value problems with anisotropic variable exponents. Communications on Pure and Applied Analysis 14:3, pages 881-896.
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Anass Ourraoui. (2015) On -Anisotropic Problems with Neumann Boundary Conditions . International Journal of Differential Equations 2015, pages 1-7.
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Nicuşor Costea & Gheorghe Moroşanu. (2012) A Multiplicity Result for an Elliptic Anisotropic Differential Inclusion Involving Variable Exponents. Set-Valued and Variational Analysis 21:2, pages 311-332.
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Guoqing Zhang & Hongtao Zhang. (2013) On a Class of Anisotropic Nonlinear Elliptic Equations with Variable Exponent. Journal of Function Spaces and Applications 2013, pages 1-9.
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Maria-Magdalena Boureanu & Vicenţiu D. Rădulescu. (2012) Anisotropic Neumann problems in Sobolev spaces with variable exponent. Nonlinear Analysis: Theory, Methods & Applications 75:12, pages 4471-4482.
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