On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications. (English) Zbl 1143.35037
In this paper the authors recall, survey and strenghten properties of \( W_0^{1,\infty }\)-truncations of \(W_0^{1,p}\)-functions that are useful from the point of view of existence theory concerning nonlinear PDE’s. One illustrates the potential of this tool by establishing the weak stability for the system of \(p\)-Laplace equations with very general right-hand sides. Then one studies the properties of Lipschitz truncations of Sobolev functions with constant and variable exponent. As non-trivial applications the Lipschitz truncations are utilized to provide a simplified proof of an existence result for incompressible power-law like fluids. New existence results are established to a class of incompressible electro-rheological fluids.
Reviewer: Adrian Carabineanu (Bucureşti)
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35J70 | Degenerate elliptic equations |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
Keywords:
Lipschitz truncation of \(W_0^{1,p}\)-functions; weak solution; power-law fluid; electro-rheological fluidReferences:
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