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Zbl 0783.49014
Amar, Micol; De Cicco, Virginia
(Cicco, V. de)
The uniqueness as a generic property for some one-dimensional segmentation problems. (English)
[J] Rend. Semin. Mat. Univ. Padova 88, 151-173 (1992). ISSN 0041-8994

The authors study the problem of minimizing the functionals $$F\sb 1(u)= \alpha \int\vert u'(x)\vert\sp 2 dx+ \beta \int \vert u(x)- g(x)\vert\sp 2 dx+ \gamma N,\quad F\sb 2(u)=\int\vert u(x)- g(x)\vert\sp 2 dx+ \gamma N,$$ where the integrals are taken over $(0,1)$, $\alpha$, $\beta$, $\gamma$ are positive constants, $N$ is the number of jumps of $u$. Such problems have in general several solutions. However, generically, the uniqueness holds.
[Yu.V.Egorov (Toulouse)]

MSC 2000:: *49Q10 Optimization of the shape other than minimal surfaces

Keywords: one-dimensional segmentation; uniqueness

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