Hölder Continuity of Weak Solutions to Certain Nonlinear Parabolic Systems in Two Space Dimensions

Joerg Wolf

A chapter in Applied Nonlinear Analysis, 2002, pp 531-546 from Springer

Abstract: Abstract In the present paper we prove the Hölder continuity of weak solutions to a nonlinear parabolic system in two space dimensions $$ \frac{{\partial u^i }} {{\partial t}} - D_\alpha a_i^\alpha (x,t,\nabla u) = B_i (x,t,u,\nabla u) in Q (i = 1,...,N) $$ (Q = Ω × (0, T), Ω ⊂ ℝ2) where the coefficients a i α (x,t,ξ)(α = 1,2;i = 1,...,N) are measurable in x, continuous in t, and Lipschitz continuous in ξ whereas the right hand side Bi satisfies the controlled growth condition.

Keywords: Nonlinear parabolic systems; controlled growth; Holder continuity (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-306-47096-7_36

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DOI: 10.1007/0-306-47096-9_36

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