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Liouville type condition and the interior regularity of quasilinear parabolic system (the case of BMO-solutions). (English) Zbl 0655.35036
The Liouville property of a quasilinear parabolic system implies the regularity of this system also in case that both the Liouville condition and the regularity of the system are formulated for the weak solutions with finite BMO-seminorms. On the other hand (again in the framework of BMO) from the slightly modified condition of the regularity of the system it follows that this system has the Liouville property.
MSC:
35K55 Nonlinear parabolic equations
35B65 Smoothness and regularity of solutions to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
35K10 Second-order parabolic equations
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