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1.
Antnio Ornelas 《Journal of Mathematical Analysis and Applications》2004,300(2):889-296
We prove Lipschitz regularity for a minimizer of the integral , defined on the class of the AC functions having x(a)=A and x(b)=B. The Lagrangian may have L(s,) nonconvex (except at ξ=0), while may be non-lsc, measurability sufficing for ξ≠0 provided, e.g., L**() is lsc at (s,0) s. The essential hypothesis (to yield Lipschitz minimizers) turns out to be local boundedness of the quotient φ/ρ() (and not of L**() itself, as usual), where φ(s)+ρ(s)h(ξ) approximates the bipolar L**(s,ξ) in an adequate sense. Moreover, an example of infinite Lavrentiev gap with a scalar 1-dim autonomous (but locally unbounded) lsc Lagrangian is presented. 相似文献
2.
Donglong Li Zhengde Dai Xuhong Liu 《Journal of Mathematical Analysis and Applications》2007,330(2):934-948
In this paper, the two-dimensional generalized complex Ginzburg–Landau equation (CGL)
ut=ρu−Δφ(u)−(1+iγ)Δu−νΔ2u−(1+iμ)|u|2σu+αλ1(|u|2u)+β(λ2)|u|2