We extend a celebrated identity by P. Pucci and J. Serrin, concerning C^2 solutions of Euler equations of functionals of the calculus of variations, to the case of C^1 solutions under the only additional assumption of strict convexity in the gradient. Some particular cases in which the mere convexity is sufficient are also considered.
Degiovanni, M., Musesti, A., Squassina, M., On the regularity of solutions in the Pucci-Serrin identity, <<CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS>>, 2003; 18 (3): 317-334. [doi:10.1007/s00526-003-0208-y] [http://hdl.handle.net/10807/86907]
On the regularity of solutions in the Pucci-Serrin identity
Degiovanni, Marco;Musesti, Alessandro;Squassina, Marco
2003
Abstract
We extend a celebrated identity by P. Pucci and J. Serrin, concerning C^2 solutions of Euler equations of functionals of the calculus of variations, to the case of C^1 solutions under the only additional assumption of strict convexity in the gradient. Some particular cases in which the mere convexity is sufficient are also considered.
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