Abstract:
We consider the problem of passing to the limit in a sequence of nonlinear elliptic problems. The “limit” equation is known in advance, but it has a nonclassical structure; namely, it contains the p-Laplacian with variable exponent p=p(x). Such equations typically exhibit a special kind of nonuniqueness, known as the Lavrent'ev effect, and this is what makes passing to the limit nontrivial. Equations involving the p(x)-Laplacian occur in many problems of mathematical physics. Some applications are included in the present paper. In particular, we suggest an approach to the solvability analysis of a well-known coupled system in non-Newtonian hydrodynamics (“stationary thermo-rheological viscous flows”) without resorting to any smallness conditions.
Keywords:p(x)-Laplacian, compensated compactness, weak convergence of flows to a flow.
Citation:
V. V. Zhikov, “On the Technique for Passing to the Limit in Nonlinear Elliptic Equations”, Funktsional. Anal. i Prilozhen., 43:2 (2009), 19–38; Funct. Anal. Appl., 43:2 (2009), 96–112
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\paper On the Technique for Passing to the Limit in Nonlinear Elliptic Equations
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\pages 19--38
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\yr 2009
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\pages 96--112
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Linking options:
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