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Le, Dung

Regularity for fully nonlinear \(p\)-Laplacian parabolic systems: the degenerate case. (English) Zbl 1357.35180

Adv. Nonlinear Stud. 14, No. 1, 199-237 (2014).
Summary: This paper studies Hölder regularity property of bounded weak solutions to a class of strongly coupled degenerate parabolic systems.

MSC:

35K51 Initial-boundary value problems for second-order parabolic systems
35B65 Smoothness and regularity of solutions to PDEs
35K59 Quasilinear parabolic equations
35K65 Degenerate parabolic equations
35K92 Quasilinear parabolic equations with \(p\)-Laplacian
49J20 Existence theories for optimal control problems involving partial differential equations

Keywords:

optimal mass transport; \(p\)-Laplacian equations; thin domains
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References:

[1] Le, Global existence for a class of triangular parabolic systems on domains of arbitrary dimension Proc no pp, Amer Math Soc 7 pp 133– (2005)
[2] Le, Global existence for a class of strongly coupled parabolic systems no pp, Appl pp 185– (2006)
[3] Le, Partial regularity of solutions to a class of strongly coupled degenerate parabolic systems Discrete suppl pp, Syst pp 2005–
[4] Kinnunen, Higher integrability for parabolic systems of p - Laplacian type Duke No pp, Math J pp 102– (2000)
[5] Giaquinta, On the partial regularity of weak solutions of nonlinear parabolic systems pp, Math pp 179– (1982) · Zbl 0469.35028
[6] Kalita, On Holder continuity of solutions of nonlinear parabolic systems Comment pp, Math Carol pp 35– (1994)
[7] Arkhipova, On a Partial Regularity up to the Boundary of Weak Solutions to Quasilinear Parabolic Systems with Quadratic Growth Zap pp, Inst pp 249– (1997) · Zbl 0969.35032
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