1,720,998 research outputs found
The decomposable sets of measurable functions: some properties and applications to maltivalued maps
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Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)
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On the Validity of the Euler–Lagrange Equation
No full textAbstractUnder some regularity assumptions on the boundary datum u0 (assumptions automatically satisfied in the classical case when the growth of the integrand is bounded by a+b‖ξ‖p), we prove the validity of the Euler–Lagrange equation for the functional∫Ω[f(‖∇u(x)‖)+g(x, u(x))]dxunder general growth assumptions on f, for instance for f(‖ξ‖)=P(‖ξ‖)eK‖ξ‖ with P a nontrivial polynomial and K⩾0, or for f (‖ξ‖)=‖ξ‖‖ξ‖
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