Optimization problems on general classes of rearrangements. (English) Zbl 1219.35066
Summary: This paper is concerned with maximization and minimization problems of the energy integral associated to \(p\)-Laplace equations depending on functions that belong to a class of rearrangements. We prove existence and uniqueness results, and present some features of optimal solutions. The radial case is discussed in detail. We also prove a result of uniqueness for a class of \(p\)-Laplace equations under non-standard assumptions.
MSC:
| 35J20 | Variational methods for second-order elliptic equations |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 49K20 | Optimality conditions for problems involving partial differential equations |
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