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The validity of the Euler-Lagrange equation for solutions to variational functionals with fast growth
Abstract
For L convex and defined on R^{N}, we consider a solution u to the problem of minimizing ∫_{Ω}L(∇v(x))dx. We provide a growth condition on L to guarantee that u is locally bounded and, by building suitable variations, we prove the validity of the Euler-Lagrange equation without imposing further regularity on L.
Keywords
Calculus of variations, Euler-Lagrange equation, boundedness of the solution.
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PDFDOI: http://dx.doi.org/10.14510%2Flm-ns.v33i1.28