We prove the validity of the EulerLagrange equation for the class of functionals of the type ∫Ω[L(∇u)+g(x,u)]dx, where u→g(x,u) is a concave function. Our result is based on a recent paper by Degiovanni and Marzocchi (2009) [6], where no growth assumptions on L are needed. © 2010 Elsevier Ltd. All rights reserved.
Bonfanti, G., Mazzola, M. (2010). On the Validity of the Euler-Lagrange Equation in a Nonlinear Case. NONLINEAR ANALYSIS, 73(1), 266-269 [10.1016/j.na.2010.03.020].
On the Validity of the Euler-Lagrange Equation in a Nonlinear Case
BONFANTI, GIOVANNI
;MAZZOLA, MARCO
2010
Abstract
We prove the validity of the EulerLagrange equation for the class of functionals of the type ∫Ω[L(∇u)+g(x,u)]dx, where u→g(x,u) is a concave function. Our result is based on a recent paper by Degiovanni and Marzocchi (2009) [6], where no growth assumptions on L are needed. © 2010 Elsevier Ltd. All rights reserved.
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