Plane-like minimizers in periodic media: jet flows and by Valdinoci E.

By Valdinoci E.

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Extra info for Plane-like minimizers in periodic media: jet flows and Ginzburg-Landau-type functionals

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On the theory of superconductivity, Zh. E`ksper. Teoret. Fiz. 20 (1950), 1064–1082. Ginzburg, V. , Pitaevskiı˘, L. , On the theory of superfluidity, Sov. Phys. JETP 34/7 (1958), 858–861. , Minimal surfaces and functions of bounded variation, Monogr. Math. 80, Birkha¨user-Verlag, Basel-Boston, Mass. 1984. , Metodi diretti nel calcolo delle variazioni, Unione Matematica Italiana, Bologna 1994. Gurtin, M. , On a theory of phase transitions with interfacial energy, Arch. Rat. Mech. Anal. 87 (1985), no.

Close to À1, and let y A ½Ày0 ; y0 Š, with y ? e Ày0 . Then 178 Valdinoci, Plane-like minimizers in periodic media m 0 e L n ðfu > yg X BK Þ e L n ðfu > y ? g X BK Þ; therefore, using the result for y ? , our hypotheses on F and (i), we infer that Cr n e L n ðfu > y ? g X Br Þ e L n ðfu > yg X Br Þ þ L n ðfy ? < u e yg X Br Þ Ð 1 F inf? F Br e L n ðfu > yg X Br Þ þ u A ½y ; y0 Š e L n ðfu > yg X Br Þ þ Cr nÀ1 ; and so L n ðfu > yg X Br Þ f Cr n . From these consideration, in the rest of the proof, we may and do assume that y is close to À1.

Math. 35 (1982), no. 1, 29–68. Alt, H. , Ca¤arelli, L. , A free boundary problem for quasilinear elliptic equations, Ann. Scu. Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), no. 1, 1–44. Alt, H. , Ca¤arelli, L. , Jets with two fluids. I. One free boundary, Indiana Univ. Math. J. 33 (1984), no. 2, 213–247. , Laminations of 3-tori by least area surfaces, Analysis, et cetera, Academic Press, Boston, MA (1990), 85–114. , Some Results on Surface Measures in Calculus of Variations, Ann. Mat. Pura Appl. (4) 170 (1996), 329–359.

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