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Hölder regularity of the gradient for the non‐homogeneous parabolic p ( x , t )‐Laplacian equations
Author(s) -
Yao Fengping
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2953
Subject(s) - mathematics , homogeneous , hölder condition , laplace operator , mathematical analysis , parabolic partial differential equation , p laplacian , pure mathematics , combinatorics , partial differential equation , boundary value problem
In this paper, we obtain the local Hölder regularity of the gradient of weak solutions for the non‐homogeneous parabolic p ( x , t )‐Laplacian equationsu t − divA ∇ u ⋅ ∇ up ( x ) − 2 2A ∇ u = div | f | p ( x ) − 2 f , provided p ( x , t ), A and f are Hölder continuous functions. Copyright © 2013 John Wiley & Sons, Ltd.