Existence and L^s ∩ W^{1,q} regularity are shown for solutions to the given parabolic-elliptic system with f in L1(Ω_T) and |u|^θ source, for θ in (0,2/N).
Simon,Compact sets in the spaceL p(0, T;B), Annali di Matematica Pura ed Applicata146(1986), 65–96
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Existence and regularity of solutions to parabolic-elliptic nonlinear systems
Existence and L^s ∩ W^{1,q} regularity are shown for solutions to the given parabolic-elliptic system with f in L1(Ω_T) and |u|^θ source, for θ in (0,2/N).