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- W781736791 abstract "over some class of real-valued functions on the domain Ω⊂R. To answer basic questions about the minima, such as existence, uniqueness, and regularity, appropriate structure must be placed on the function F and on the underlying function space in which the minimization occurs. In the simple case F (x, z, p) = (1 + |p|), where m > 1 is a constant, Ladyzhenskaya and Ural’tseva [21] proved complete results. A key element of their analysis is that the Euler–Lagrange equation for I is uniformly elliptic. We write this equation as div((1 + |Du|2)(m−2)/2Du) = 0 or as (0.1) a(Du)Diju = 0 , where a(p) = (1 + |p|2)(m−2)/2 [ δ + (m− 1)pp 1 + |p|2 ] ." @default.
- W781736791 created "2016-06-24" @default.
- W781736791 creator A5015371533 @default.
- W781736791 date "1992-01-01" @default.
- W781736791 modified "2023-10-12" @default.
- W781736791 title "On the natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva" @default.
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- W781736791 doi "https://doi.org/10.4064/-27-2-295-308" @default.
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