Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator
In this paper we consider an unconstrained and a constrained minimization problem related to the boundary value problem −∆pu = f in D, u = 0 on ∂D. In the unconstrained problem we minimize an energy functional relative to a rearrangement class, and prove existence of a unique solution. We also con...
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| Format: | Article |
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The Hebrew University Magnes Press
2015
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| Online Access: | https://eprints.nottingham.ac.uk/50884/ |
| Summary: | In this paper we consider an unconstrained and a constrained minimization problem related to the boundary value problem
−∆pu = f in D, u = 0 on ∂D.
In the unconstrained problem we minimize an energy functional relative to a rearrangement class, and prove existence of a unique solution. We also consider the case when D is a planar disk and show that the minimizer is radial and increasing. In the constrained problem we minimize the energy functional relative to the intersection of a rearrangement class with an affine subspace of codimension one in an appropriate function space. We briefly discuss our motivation for studying the constrained minimization problem. |
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