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A free boundary problem related to thermal insulation. (English) Zbl 1351.35268
The scope of the paper is to study a variational problem, that can be associated to a free boundary problem, which arises in matters connected to “thermal insulation”. The particular feature of this set optimization problem is that the boundary of the set to be optimized is not a level surface of a harmonic function, but rather a surface along which an harmonic function complies with a Robin boundary condition.

35R35 Free boundary problems for PDEs
49Q20 Variational problems in a geometric measure-theoretic setting
Full Text: DOI arXiv
[1] Caffarelli L.A., Ann. Scuola Norm. Sci 14 pp 355– (1987)
[2] Alt H.W., J. Reine Angew. Math 325 pp 105– (1981)
[3] Ambrosio L., Functions of bounded variation and free discontinuity problems (2000) · Zbl 0957.49001
[4] DOI: 10.1007/978-3-0348-9244-5_8
[5] DOI: 10.1007/s00205-013-0671-3 · Zbl 1283.49056
[6] David, G. (2005).Singular Sets of Minimizers for the Mumford–Shah Functional, Vol. 233, Progress in Mathematics. Basel: Birkhäuser Verlag. · Zbl 1086.49030
[7] DOI: 10.1016/S0294-1449(02)00097-5 · Zbl 1038.49022
[8] David, G., Semmes, S. (1993).Analysis of and on Uniformly Rectifiable Sets, Vol. 38, Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society. · Zbl 0832.42008
[9] DOI: 10.1007/BF01052971 · Zbl 0682.49002
[10] DOI: 10.1007/BF01236935 · Zbl 0094.26301
[11] Giusti, E. (1984).Minimal Surfaces and Functions of Bounded Variation, Vol. 80, Monographs in Mathematics. Basel: Birkhäuser Verlag. · Zbl 0545.49018
[12] John, F. (1948). Extremum problems with inequalities as subsidiary conditions. In:Studies and Essays Presented to R. Courant on his 60th Birthday.New York: Interscience Publishers, Inc., pp. 187–204.
[13] DOI: 10.1016/S0021-7824(99)00019-7 · Zbl 0942.49030
[14] DOI: 10.1002/cpa.3160420503 · Zbl 0691.49036
[15] Simon L., J. Diff. Geom 26 pp 327– (1987) · Zbl 0625.53052
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