Affiliation:
1. Rua Romão Ramalho 59, 7000-671 , Évora , Portugal .
Abstract
Abstract
This paper concerns minimization problems from Calculus of Variations rotationally invariant with respect to the gradient. Inspired by properties associated with results which are valid for elliptic partial differential equations, it presents some local estimates nearby non extremum points as well as nearby extremum points for these problems, generalizing some results obtained by Arrigo Cellina, Vladimir V. Goncharov and myself. As a consequence, some local estimates are obtained for the difference between the supremum and the infimum of any solution to the problem considered.
Reference8 articles.
1. [1] A. Cellina, Uniqueness and comparison results for functionals depending on u and ∇u, SIAM J. Control Optim. 46(3) (2007), 711-716.10.1137/060657455
2. [2] A. Cellina, On the strong maximum principle, Proc. Amer. Math. Soc. 130 (2002), 413-418.10.1090/S0002-9939-01-06104-4
3. [3] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd Edition, Springer, 1998.
4. [4] V. V. Goncharov and T. J. Santos, Local estimates for minimizers of some convex integral functional of the gradient and the strong maximum principle, Set-Valued and Var. Anal. 19 (2011), 179-202.10.1007/s11228-011-0176-x
5. [5] V. V. Goncharov and T. J. Santos, An extremal property of the inf- and sup- convolutions regarding the strong maximum principle, Proceedings of the 8th Congress of the International Society for Analysis, its Applications and Computation 2 (2012), 185-195.