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Regularity in free boundary problems. (English) Zbl 0352.35023

MSC:
35D10 Regularity of generalized solutions of PDE (MSC2000)
35J25 Boundary value problems for second-order elliptic equations
35K20 Initial-boundary value problems for second-order parabolic equations
35J60 Nonlinear elliptic equations
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References:
[1] S. Agmon - A. Douglis - L. Nirenberg , Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions , I, Comm. Pure Appl. Math. , 12 ( 1959 ), pp. 623 - 727 . MR 125307 | Zbl 0093.10401 · Zbl 0093.10401
[2] C. Baiocchi , Su un problema a frontiera libera connesso a questioni di idraulica , Ann. di Mat. Pura e Applic. , 92 ( 1972 ), pp. 107 - 127 . MR 408443 | Zbl 0258.76069 · Zbl 0258.76069
[3] H. Brézis - D. Kinderlehrer , The smoothness of solutions to nonlinear variational inequalities , Indiana Univ. Math. J. , 23 ( 1973 -74), pp. 831 - 844 . MR 361436 | Zbl 0278.49011 · Zbl 0278.49011
[4] H. Brézis - G. Stampacchia , The hodograph method in fluid dynamics in the light of variational inequalities , Arch. Rat. Mech. and Anal. , 61 ( 1976 ), pp. 1 - 18 . MR 477505 | Zbl 0334.76004 · Zbl 0334.76004
[5] L.A. Caffarelli , The smoothness of the free boundary in a filtration problem , to appear. · Zbl 0388.35010
[6] L.A. Caffarelli , The regularity of elliptic and parabolic free boundaries , Bull. A.M.S. , 82 ( 1976 ), pp. 616 - 618 . Article | MR 404862 | Zbl 0357.35011 · Zbl 0357.35011
[7] L.A. Caffarelli - N. Rivière , Smoothness and analyticity of free boundaries in variational inequalities , Ann. Scuola Norm. Sup. Pisa , 3 ( 1976 ), pp. 289 - 310 . Numdam | MR 412940 | Zbl 0363.35009 · Zbl 0363.35009
[8] R. Finn , Capillarity phenomena , Usp. Akad. Nauk , 29 ( 1974 ), pp. 131 - 152 ; Engl. trans. in Russian Math. Surveys , 29 ( 1974 ), pp. 133 - 153 . MR 484001 | Zbl 0341.76013 · Zbl 0341.76013
[9] A. Friedman , Partial differential equations of parabolic type , Prentice-Hall , Englewood Cliffs, N. J. , 1964 . MR 181836 | Zbl 0144.34903 · Zbl 0144.34903
[10] A. Friedman , Analyticity of the free boundary for the Stefan problem , Arch. Rat. Mech. and Anal. , 61 ( 1976 ), pp. 97 - 125 . MR 407452 | Zbl 0329.35034 · Zbl 0329.35034
[11] K.O. Friedrichs , Über ein Minimumproblem für Potentialströmungen mit freiem Rande , Math. Ann. , 109 ( 1934 ), pp. 60 - 82 . MR 1512880 | Zbl 0008.16605 | JFM 59.1447.01 · Zbl 0008.16605
[12] P.R. Garabedian - H. Lewy - M. Schiffer , Axially symmetric cavitational flow , Ann. Math. , 56 ( 1952 ), pp. 560 - 602 . MR 53684 | Zbl 0047.18203 · Zbl 0047.18203
[13] C. Gerfiardt , Regularity of solutions of nonlinear variational inequalities , Arch. Rat. Mech. Anal. , 52 ( 1973 ), pp. 389 - 393 . MR 377262 | Zbl 0277.49003 · Zbl 0277.49003
[14] D. Kinderlehrer , Elliptic variational inequalities , Proc. Intl. Congress of Math. Vancouver , 1974 , pp. 269 - 273 . MR 463684 | Zbl 0356.35023 · Zbl 0356.35023
[15] D. Kinderlehrer , The free boundary determined by the solution to a differential equation , Indiana Univ. Math. Jour. , 25 ( 1976 ), pp. 195 - 208 . MR 393807 | Zbl 0336.35031 · Zbl 0336.35031
[16] D. Kinderlehrer - L. Nirenberg , Regularity of free boundaries , Conf. del Seminario di Mat., Univ. di Bari , to appear. Zbl 0361.35012 · Zbl 0361.35012
[17] H. Lewy , A priori limitations for the solutions of the Monge-Ampère equations, II , Trans. A.M.S. , 41 ( 1937 ), pp. 365 - 374 . MR 1501906 | Zbl 0017.21101 | JFM 63.0442.01 · Zbl 0017.21101
[18] H. Lewy , On minimal surfaces with partially free boundaries , Comm. Pure Appl. Math. , 4 ( 1951 ), pp. 1 - 13 . MR 52711 · Zbl 0042.15702
[19] H. Lewy , The nature of the domain governed by different regimes, Atti del Convegno Internazionale Metodi valutativi nella fisica-matematica , Accad. Naz. dei Lincei ( 1975 ), pp. 181 - 188 .
[20] H. Lewy - G. Stampacchia , On the regularity of the solution to a variational inequality , Comm. Pure Appl. Math. , 22 ( 1969 ), pp. 153 - 188 . MR 247551 | Zbl 0167.11501 · Zbl 0167.11501
[21] C.B. Morrey Jr. , Multiple integrals in the calculus of variations , Springer , New York - Berlin , 1966 . MR 202511 | Zbl 0142.38701 · Zbl 0142.38701
[22] D. Riabouchinsky , Sur un problème de variation , C. R. Acad. Sci. Paris , 185 ( 1927 ), pp. 840 - 841 . JFM 53.0784.02 · JFM 53.0784.02
[23] D.G. Schaeffer , Some examples of singularities in a free boundary , Ann. Scuola Norm. Sup. Pisa , 4 ( 1977 ), pp. 133 - 144 . Numdam | MR 516201 | Zbl 0354.35033 · Zbl 0354.35033
[24] L. Simon - J. Spruck , Existence and regularity of a capillary surface with prescribed contact angle , Arch, Rat. Mech. and Anal. , 61 ( 1976 ), pp. 19 - 34 . MR 487724 | Zbl 0361.35014 · Zbl 0361.35014
[25] V.A. Solonnikov , On boundary value problems for linear parabolic systems of differential equations of general type , Trudii Math. Inst. Steklov , 83 ( 1965 ); Engl. transl. A.M.S . in Boundary value problems of mathematical physics, III , ed. by O. A. LADYZHENSKAYA, 1967 . MR 211083 | Zbl 0164.12502 · Zbl 0164.12502
[26] G. Stampacchia , Variational inequalities , Proc. Int. Congress of Mathematicians, Nice , 1970 , pp. 877 - 883 . MR 513209 | Zbl 0241.35001 · Zbl 0241.35001
[27] J.J. Stoker , Water Waves , Interscience - Wiley , New York , 1957 . MR 1153414 | Zbl 0078.40805 · Zbl 0078.40805
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