首页|Partial regularity and nonlinear potential estimates for Stokes systems with super-quadratic growth
Partial regularity and nonlinear potential estimates for Stokes systems with super-quadratic growth
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This paper builds a bridge between partial regularity theory and nonlinear potential theory for the following generalized stationary Stokes system with super-quadratic growth and continuous coefficients:-div A(x,Du)+▽π=f,divu=0,where Du is the symmetric part of the gradient ▽u.We first establish an e-regularity criterion involving both the excess functional of the symmetric gradient Du and Wolff potentials of the nonhomogeneous term f to guarantee the local vanishing mean oscillation(VMO)-regularity of Du in an open subset Ωu of Ω with full measure.Such an e-regularity criterion leads to a pointwise Wolff potential estimate of Du,which immediately infers that Du is partially C0-regular under appropriate assumptions.Finally,we give a local continuous modulus estimate of Du.
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