Displaying similar documents to “Static Hedging of Barrier Options with a Smile: An Inverse Problem”

An optimal matching problem

Ivar Ekeland (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Given two measured spaces ( X , μ ) and ( Y , ν ) , and a third space , given two functions  and , we study the problem of finding two maps s : X Z and t : Y Z such that the images s ( μ ) and t ( ν ) coincide, and the integral X u ( x , s ( x ) ) d μ - Y v ( y , t ( y ) ) d ν is maximal. We give condition on and for which there is a unique solution.

On Some Nonlinear Partial Differential Equations Involving the “1”-Laplacian and Critical Sobolev Exponent

Françoise Demengel (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Let Ω be a smooth bounded domain in 𝐑 n , n > 1, let a and f be continuous functions on Ω ¯ , 1 = n n - 1 . We are concerned here with the existence of solution in B V ( Ω ) , positive or not, to the problem:
 - div σ + a ( x ) s i g n u a m p ; = f | u | 1 - 2 u σ . u a m p ; = | u | in Ω u is not identically zero , a m p ; - σ . n ( u ) = | u | on Ω . This problem is closely related to the extremal functions for the problem of the best constant of W 1 , 1 ( Ω ) into L N N - 1 ( Ω ) .