Entropy solutions for the p(x)-Laplace equation

By Manel Sanchón, José Miguel Urbano. 2009

157 citations recorded by the source corpus.

CMUC/FCT and MCYT grants BMF2002- 04613-C03, MTM2005-07660-C02 (first author); CMUC/FCT and Project POCI/MAT/57546/2004 (second author)

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5002106b699a849f0343b00d699cd0e49e7fa069

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In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Ciqiang Zhuo
4. Jun Liu
5. Piotr Gwiazda
6. Iwona Chlebicka
7. P. Hasto
8. Petra Wittbold

In Computational Theory and Mathematics

1. Piotr Gwiazda
2. P. Hasto
3. A. Zimmermann
4. Petra Wittbold
5. Dachun Yang
6. Iwona Chlebicka
7. Ciqiang Zhuo
8. Wen Yuan

Citations in the corpus

• Renormalized solutions for a nonlinear parabolic equation with variable exponents and l(1)-data (2010, background): “For p ∈ C(Ω) with 1 < p− p+ < N existence and uniqueness of a renormalized solution of (E)( f ) has been proved for any f ∈ L1(Ω) (see also [32] for results in the case 1 < p− p+ < N for the case of a log-continuous exponent and [7] for regularity properties of renormalized solutions in the case p− ”
• Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, background): “In addition, the theory of variable function spaces also has interesting applications in fluid dynamics [2], image processing [17], partial differential equations and variational calculus [3, 30, 40, 65].”
• Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces (2012, background): “For results on existence of renormalized solutions of elliptic problems of type (E, f) with a(·, ·) satisfying a variable growth condition we refer to [20], [43] (for related results see also [9], [10], [42]).”
• Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “Apart from theoretical considerations, such function spaces have interesting applications in fluid dynamics [1, 57], image processing [7], partial differential equations and variational calculus [2, 20, 25, 54, 58].”
• Quasilinear elliptic problems with nonstandard growth. (2011, methodology): “In the second inequality above we have used [2].”
• Overview of differential equations with non-standard growth (2010, background): “[128] Henriques, E.; Urbano, J.M.: Intrinsic scaling for PDE’s with an exponential nonlinearity.”
• The obstacle problem for nonlinear elliptic equations with variable growth and L1-data (2008, methodology): “Proof. (i) We proceed as in the proof of Proposition 3.2 in [ 31 ], sketching here only the main steps (we refer to [31] for a complete account of the details).”