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This paper is devoted to some applications of a weighted symmetrization inequality related to a second order boundary value problem. We first interpret the inequality in the context of elastic membranes, and observe that it lends itself to make a comparison between the deflection of a membrane with a varying density with that of a membrane with a uniform… (More)
We consider an inverse rearrangement semilinear partial differential equation in a 2-dimensional ball and show that it has a unique maximizing energy solution. The solution represents a confined steady flow containing a vortex and passing over a seamount. Our approach is based on a rearrangement variational principle extensively developed by G. R. Burton.
This note extends the results in , by describing the dependence of the optimal constant in the p-version of Friedrichs' inequality on the boundary integral term. In particular, it is shown that this constant is continuous, increasing, concave and increases to the optimal constant for the Dirichlet problem as s → ∞.
In this note we use the Nehari manifold and fibering maps to show existence of positive solutions for a nonlinear biharmonic equation in a bounded smooth domain in R n , when n = 5, 6, 7.
In this note we introduce a variational problem with respect to an integrable fuzzy set f. The energy functional is maximized over a deleted σ-algebra. Using the decreasing rearrangement of f we prove that the admissible set can be replaced by the more convenient set of cuts of f. Finally an special case is considered where the variational problem can be… (More)