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Existence of solutions of the parabolic variational inequality with variable exponent of nonlinearity. (English) Zbl 1208.49007

Summary: New properties of variable exponent Lebesgue and Sobolev spaces are examined. Using these properties we prove the existence of the solution of some parabolic variational inequality.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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