Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence
We consider the following problem: given a bounded convex domain ω ⊂ ℝN we consider the limit as p →∞ of solutions to (Equation Presented) Under appropriate assumptions on the coefficients b<inf>p</inf> that in particular verify that lim<inf>p→∞</inf> b<inf>p</inf>...
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| Autores principales: | , , |
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| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_21919496_v3_n3_p133_Mazon |
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| Sumario: | We consider the following problem: given a bounded convex domain ω ⊂ ℝN we consider the limit as p →∞ of solutions to (Equation Presented) Under appropriate assumptions on the coefficients b<inf>p</inf> that in particular verify that lim<inf>p→∞</inf> b<inf>p</inf> = b uniformly in Ω¯, we prove that there is a uniform limit of u<inf>pj</inf> (along a sequence pj →∞) and that this limit is a Kantorovich potential for the optimal mass transport problem of f<inf>+</inf> to f<inf>-</inf> with cost c(x, y) given by the formulac(x, y) = inf<inf>σ(0)=x,σ(1)=y</inf> f<inf>σ</inf>bds. |
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