Calculus of Variations and Geometric Measure Theory
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A. Cellina - A. Ferriero

Existence of Lipschitz solutions to the classical problem of the calculus of variations in the autonomous case

created by ferrieroa on 19 Apr 2007


Published Paper

Inserted: 19 apr 2007

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Volume: 20
Number: 6
Pages: 374-384
Year: 2003


Under general growth assumptions, that include some cases of linear growth, we prove existence of Lipschitzian solutions to the problem of minimizing $\int_{a}^{b}L(x(s),x^{\prime}(s))ds$ with the boundary conditions $x(a)=A,x(b)=B$.


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