×

zbMATH — the first resource for mathematics

Nonlinear desingularization in certain free-boundary problems. (English) Zbl 0454.35087

MSC:
35R35 Free boundary problems for PDEs
35J99 Elliptic equations and elliptic systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abrikosov, A.A.: On the magnetic properties of superconductors of the second group. Sov. Phys. JETP5, 1174–1182 (1957)
[2] Adler, S.L.: Global structure of static Euclidean SU(2) solutions. Phys. Rev. D20, 1386–1411 (1979) · doi:10.1103/PhysRevD.20.1386
[3] Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math.12, 623–727 (1959) · Zbl 0093.10401 · doi:10.1002/cpa.3160120405
[4] Berger, M.S.: A bifurcation theory for nonlinear elliptic partial differential equations. In: Bifurcation theory and nonlinear eigenvalue problems (eds. J. B. Keller, S. Antman), pp. 113–216. New York: Benjamin 1969
[5] Berger, M.S.: Nonlinearity and functional analysis. New York: Academic Press 1977 · Zbl 0368.47001
[6] Fraenkel, L.E.: On steady vortex rings of small cross-section in an ideal fluid. Proc. R. Soc. London A316, 29–62 (1970) · Zbl 0195.55101 · doi:10.1098/rspa.1970.0065
[7] Fraenkel, L.E.: A lower bound for electrostatic capacity in the plane. Proc. R. Soc. Edinburgh, Sect. A, to appear · Zbl 0466.31007
[8] Fraenkel, L.E., Berger, M.S.: A global theory of steady vortex rings in an ideal fluid. Acta Math.132, 13–51 (1974) · Zbl 0282.76014 · doi:10.1007/BF02392107
[9] Keady, G., Norbury, J.: A semilinear elliptic eigenvalue problem. I, II. Proc. R. Soc. Edinburgh, A, to appear · Zbl 0452.35031
[10] Ladyzhenskaya, O.A., Ural’tseva, N.N.: Linear and quasilinear elliptic equations. New York: Academic Press 1968 · Zbl 0164.13002
[11] Nirenberg, L.: On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa (3)13, 115–162 (1959) · Zbl 0088.07601
[12] Norbury, J.: Steady planar vortex pairs in an ideal fluid. Commun. Pure Appl. Math.28, 679–700 (1975) · Zbl 0338.76015 · doi:10.1002/cpa.3160280602
[13] Pólya, G., Szegö, G.: Isoperimetric inequalities in mathematical physics. Princeton: Princeton University Press 1951 · Zbl 0044.38301
[14] Stampacchia, G.: Variational inequalities. Theory and applications of monotone operators. Proc. NATO Advanced Study Inst., pp. 101–192. Gubbio: Ediz. Oderisi 1969
[15] Temam, R.: A non-linear eigenvalue problem: the shape at equilibrium of a confined plasma. Arch. Ration. Mech. Anal.60, 51–73 (1976) · Zbl 0328.35069 · doi:10.1007/BF00281469
[16] Widman, K.-O.: Inequalities for Green functions of second order elliptic operators. Report 8-1972, Dept. of Math., Linköping University, Sweden 1972
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.