A free boundary problem arising in magnetohydrodynamic system
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1995)
- Volume: 22, Issue: 3, page 375-448
- ISSN: 0391-173X
Access Full Article
topHow to cite
topReferences
top- [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), 623-727. Zbl0093.10401MR125307
- [2] H.W. Alt - L.A. Caffarelli, Existence and regularity for a mimimum problem with free boundary. J. Reine Angew. Math.325 (1981), 105-144. Zbl0449.35105MR618549
- [3] H.W. Alt - L.A. Caffarelli - A. Friedman, Variational problems with two phases and their free boundaries. Trans. Amer. Math. Soc.282 (1984), 431-461. Zbl0844.35137MR732100
- [4] J. Athanasopoulos - L.A. Caffarelli, A theorem of real analysis and its application to free-boundary problems. Comm. Pure Appl. Math.38 (1985), 499-502. Zbl0593.35084MR803243
- [5] L.A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C1,α. Rev. Mat. Iberoamericana3 (1987), 139-162. Zbl0676.35085
- [6] L.A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries. Part II: Flat free boundaries are Lipschitz. Comm. Pure Appl. Math.42 (1989), 55-78. Zbl0676.35086MR973745
- [7] L.A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries. Part III: Existence theory, compactness, and dependence on X. Ann. Scuola Norm. Sup. Pisa15 (1988), 583-602. Zbl0702.35249MR1029856
- [8] L.A. Caffarelli - E. Fabes - M. Mortola - S. Salsa, Boundary behavior of non-negative solutions of elliptic operators in divergence form. Indiana Univ. Math. J.30 (1981), 621-640. Zbl0512.35038MR620271
- [9] M. Cranston - E. Fabes - Z. Zhao, Conditional gauge and potential theory for the Schrödinger operator. Trans. Amer. Math. Soc.307 (1988), 171-194. Zbl0652.60076MR936811
- [10] B. Dahlberg, On estimates of harmonic measures. Arch. Rational Mech. Anal.65 (1977), 272-288. Zbl0406.28009MR466593
- [11] H. Federer, Geometric measure theory. Springer-Verlag, Berlin, 1969. Zbl0176.00801MR257325
- [12] S. Friedland - W.K. Hayman, Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions. Comment. Math. Helv.51 (1976), 133-161. Zbl0339.31003MR412442
- [13] A. Friedman, Variational principles and free-boundary problems. Wiley-Interscience, New York, 1982. Zbl0564.49002MR679313
- [14] D. Gilbarg - N.S. Trudinger, Elliptic partial differential equations of second order. Second edition, Springer-Verlag, Berlin, 1983. Zbl0562.35001MR737190
- [15] H. Grad - A. Kadish - O. Stevens, A free boundary Tokamak equilibrium. Comm. Pure Appl. Math.27 (1974), 39-57. Zbl0283.76076MR351245
- [16] D. Jerison - C. Kenig, Boundary behavior of harmonic functions in nontangentially accessible domains. Adv. Math.46 (1982), 80-147. Zbl0514.31003MR676988
- [17] D. Kinderlehrer - L. Nirenberg - J. Spruck, Regularity in elliptic free boundary problems, I. J. Analyse Math.34 (1978), 86-119. Zbl0402.35045MR531272
- [18] D. Kinderlehrer - L. Nirenberg - J. Spruck, Regularity in elliptic free boundary problems, II: Equations of higher order. Ann. Scuola Norm. Sup. Pisa6 (1979), 637-683. Zbl0425.35097MR563338
- [19] D. Kinderlehrer - J. Spruck, Regularity in free boundary problem. Ann. Scuola Norm. Sup. Pisa5 (1978), 131-148. MR481511
- [20] C.B. Morrey, Multiple integrals in the calculus of variations. Springer-Verlag, New York, 1966. Zbl0142.38701MR202511
- [21] R. Temam, A non-linear eigenvalue problem: The shape at equilibrium of a confined plasma. Arch. Rational Mech. Anal.60 (1975), 51-73. Zbl0328.35069MR412637
- [22] R. Temam, Remarks on a free boundary value problem arising in the plasma physics. Comm. Partial Differential Equations2 (1977), 563-585. Zbl0355.35023MR602544
- [23] T. Ushijima, On the linear stability analysis of magnetohydrodynamic system. In "Lecture notes in numerical and applies systems", Vol. 5: Nonlinear Partial Differential Equations in Applied Science. Proc. U.S. - Japan Seminar, Tokyo, 1982. Editors: H. Fujita, P.D. Lax and G. Strang, North-Holland, Kinokuniya (1981), 333-344. Zbl0528.76055MR730251
- [24] Z. Zhao, Green functions and conditional gauge for a 2-dimensional domain, Seminar on Stochastic Processes, Progress in Probability and Statistics 15, Birkhäuser (1988), 283-294. Zbl0667.35065MR1046423