Regularity in free boundary problems
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 4 (1977) no. 2, p. 373-391
@article{ASNSP_1977_4_4_2_373_0,
     author = {Kinderlehrer, David and Nirenberg, Louis},
     title = {Regularity in free boundary problems},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 4},
     number = {2},
     year = {1977},
     pages = {373-391},
     zbl = {0352.35023},
     mrnumber = {440187},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1977_4_4_2_373_0}
}
Kinderlehrer, D.; Nirenberg, L. Regularity in free boundary problems. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 4 (1977) no. 2, pp. 373-391. http://www.numdam.org/item/ASNSP_1977_4_4_2_373_0/

[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

[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

[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

[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

[5] L.A. Caffarelli, The smoothness of the free boundary in a filtration problem, to appear.

[6] L.A. Caffarelli, The regularity of elliptic and parabolic free boundaries, Bull. A.M.S., 82 (1976), pp. 616-618. | MR 404862 | 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

[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

[9] A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, N. J., 1964. | MR 181836 | 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

[11] K.O. Friedrichs, Über ein Minimumproblem für Potentialströmungen mit freiem Rande, Math. Ann., 109 (1934), pp. 60-82. | JFM 59.1447.01 | MR 1512880 | 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

[13] C. Gerfiardt, Regularity of solutions of nonlinear variational inequalities, Arch. Rat. Mech. Anal., 52 (1973), pp. 389-393. | MR 377262 | Zbl 0277.49003

[14] D. Kinderlehrer, Elliptic variational inequalities, Proc. Intl. Congress of Math. Vancouver, 1974, pp. 269-273. | MR 463684 | 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

[16] D. Kinderlehrer - L. Nirenberg, Regularity of free boundaries, Conf. del Seminario di Mat., Univ. di Bari, to appear. | 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. | JFM 63.0442.01 | MR 1501906 | Zbl 0017.21101

[18] H. Lewy, On minimal surfaces with partially free boundaries, Comm. Pure Appl. Math., 4 (1951), pp. 1-13. | MR 52711

[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

[21] C.B. Morreyjr., Multiple integrals in the calculus of variations, Springer, New York - Berlin, 1966. | MR 202511 | 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

[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

[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

[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

[26] G. Stampacchia, Variational inequalities, Proc. Int. Congress of Mathematicians, Nice, 1970, pp. 877-883. | MR 513209 | Zbl 0241.35001

[27] J.J. Stoker, Water Waves, Interscience-Wiley, New York, 1957. | MR 1153414 | Zbl 0078.40805