Weak solutions to a class of parabolic systems with continuous coefficients are locally Hölder continuous almost everywhere, with a criterion for regularity points and fractional differentiability of the gradient.
Campanato, Di fferentiability of the solutions of nonlinear elliptic syste ms with natural growth, Ann
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Regularity of weak solutions to a certain class of parabolic system
Weak solutions to a class of parabolic systems with continuous coefficients are locally Hölder continuous almost everywhere, with a criterion for regularity points and fractional differentiability of the gradient.