On the Euler-lagrange Equation for a Variational Problem
نویسنده
چکیده
where g : R 7→ R strictly monotone increasing and differentiable, Ω open set with compact closure in R , and D convex closed subset of R. Under the assumption that ∇ū ∈ D a.e. in Ω, there is a unique solution u to (1.1) and we can actually give an explicit representation of u is terms of a Lax-type formula. The solution is clearly Lipschitz continuous because ∇u ∈ ∂D a.e. in Ω. The Euler-Lagrange equation for (1.1) can be written as
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