The homogeneous Dirichlet problem for non-elliptic partial differential equations with strong nonlinearities
Warnecke, Gerald G.
Commentationes Mathematicae Universitatis Carolinae, Tome 030 (1989), p. 327-346 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1989-01-01
Classification:  35G30,  35J60,  35J65,  35J70,  35Q20,  46E35 
@article{106751,
     author = {Gerald G. Warnecke},
     title = {The homogeneous Dirichlet problem for non-elliptic partial differential equations with strong nonlinearities},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {030},
     year = {1989},
     pages = {327-346},
     zbl = {0702.35061},
     mrnumber = {1014133},
     language = {en},
     url = {http://dml.mathdoc.fr/item/106751}
}

Warnecke, Gerald G. The homogeneous Dirichlet problem for non-elliptic partial differential equations with strong nonlinearities. Commentationes Mathematicae Universitatis Carolinae, Tome 030 (1989) pp. 327-346. http://gdmltest.u-ga.fr/item/106751/

Adams R. A. Sobolev spaces, Academic Press, New York, San Francisco, London, 1975. (1975) | MR 0450957 | Zbl 0314.46030

Besov O. V.; Il'In V. P.; Nikolskiñ S. M. Integral representations of functions and imbedding theorems, Vol 1, V. H. Winston k Sons, Washington D. C., 1978; [Translation of Integral'nye predstavleniya funktsij i teoremy vlozheniya, Nauka, Moskva, 1975.]. (1978) | MR 0430771

Boussinesq M. J. Théorie de l'intumescence liquide appelée onde solitaire ou de translation se propageant dans un canal reciangulaire, Comptes Rendus 72 (1871), 755-759.

Boussinesq M. J. Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des viiesses sensiblement pareilles de la surface au fond, J. Math. Pures Appl. 2 (1872), 55-108.

Brézis H.; Browder F. E. Strongly nonlinear elliptic boundary value problems, Ann. Scuola Norm. Sup. Pisa 5 (1978), 587-603. (1978) | MR 0507004

Browder F. E. Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms, Proc. Symp. Pure Math. 23 (1973), 269-286. (1973) | MR 0340815 | Zbl 0265.35035

Doppel K.; Jacob N. A non-hypoelliptic Dirichlet problem from stochastics, Ann. Acad. Sci. Fenn. Ser. A. I. Math. 8 (1983), 375-390. (1983) | MR 0731794 | Zbl 0554.35020

Dynkin E. B. Harmonic functions assocviated with several Markov processes, Adv. in Appl. Math. 2 (1981), 260-283. (1981) | MR 0626862

Friedman A. Partial differential equations, Holt, Rinehart and Winston Inc. New York 1969. Reprint Robert E. Krieger Pub. Co., Huntington - New York, 1976. (1969) | MR 0454266 | Zbl 0224.35002

Herler H. J. Entarie lineare elliptische Differentialgleichungen und anisotrope Sobolevräume: Existenz schwacher Lösungen, Z. für Anal. u. ihre Anw. 5 (1986), 223-236. (1986) | MR 0837648

Hess P. A strongly nonlinear elliptic boundary value problem, J. Math. Anal. Appl. 43 (1973), 241-249. (1973) | MR 0318670 | Zbl 0267.35039

Hörmander L. Linear partial differential operators, Die Grundlehren der mathematischen Wissenschaften 116. Springer-Verlag, Berlin - Heidelberg - New York, 1976. (1976) | MR 0248435

Jacob N. On generalized Dirichlet problems, Math. Scand. 55 (1984), 245-252. (1984) | MR 0787200 | Zbl 0538.35015

Jacob N.; Schomburg B. On Garding's inequality, Aeq. Math. 31 (1986), 7-17. (1986) | MR 0857682 | Zbl 0635.35011

Kalantarov V. K.; Ladyzhenskaya O. A. The occurence of collapse for quasilinear equations of parabolic and hyperbolic types, J. Sov. Math. 10 (1978), 53-70; [Translated from Inst. im. V. A. Steklova AN SSSR 69, 1977, 77-102]. (1978)

Kolgomorov A. N.; Fomin S. V. Reelle Funktionen und Funktionalanalysis, VEB Verlag der Wissenschaften, Berlin, 1975. (1975) | MR 0448013

Landes R. Quasilineare elliptische Differentialoperatoren mit starken Wachstum in den Termen höchster Ordnung, Math. Z. 157 (1977), 23-36. (1977) | MR 0486996

Lehtonen A. On quasiliner variational inequalities, University of Jyväskylä, Department of Mathematics Report 26 (1983). (1983) | MR 0719691

Luohivaara I. S.; Simader C. G. Über nichtelliptische lineare partielle Differentialoperatoren mit konstaten Koeffizienten, Ann. Acad. Sci. Fenn. Ser.A. I. Math. 513 (1972). (1972) | MR 0330738

Luohivaara I. S.; Simader C. G. Über das verallgemeinerte Dirichletproblem für koerzitive lineare partielle Differentialgleichungen, Ann. Acad. Sci. Fenn. Ser.A. I. Math. 2 (1976), 327-343. (1976) | MR 0473477

Moser J. Nearly integrable and integrable systems, Topics in nonlinear dynamics, AIP Conf. Proc. 46 (1978), 1-15. (1978) | MR 0526898

Natanson I. P. Theorie der Funktionen einer reellen Veränderlichen, Verlag Harri Deutsch, Thun - Frankfurt/Main, 1981. (1981) | MR 0640867 | Zbl 0464.26001

Nikol'Skii S. M. The first boundary problem for a general linear equation, Sov. Math. - Doklady 3 (1962), 1388-1390; [Translated from Dokl. Akad. Nauk SSSR 146, 1962, 767-769.]. (1962) | MR 0140823

Rákosník J. Some remarks to anisotropic Sobolev spaces I., Beiträge zur Analysis 13 (1979), 55-68. (1979) | MR 0536217

Rákosník J. Some remarks to anisotropic Sobolev spaces II., Beiträge zur Analysis 15 (1981), 127-140. (1981) | MR 0614784

Schomburg B. Das verallgemeinerte homogene Dirichlet - Problem für Produkte elliptischer Differentialoperatoren zweiter Ordnung, Dissertation, Freie Universität Berlin, 1985. (1985)

Showalter R. E. Hubert space methods for partial differential equations, Pitman Publ. Ltd., London, 1979. (1979) | MR 0477394

Simader C. G. Über achwache Lösungen des Dirichletproblems für streng nichtlineare elliptische Differentialgleichungen, Math. Z. 150 (1976), 1-26. (1976) | MR 0420001

Tafel W. Relative Beschränktheit und maximale Differentialoperatoren, Dissertation an der Fakulät für Mathematik der Ludwig-Maximilians-Universität München, 1979. (1979)

Vainberg M. M. Variational methods for the study of nonlinear operators, Holden Day Inc., San Francisco - London - Amsterdam, 1964; [Translation of variatsionnye metody issledovaniya nelineinykh operatorov, Moscow, 1956.]. (1964) | MR 0176364 | Zbl 0122.35501

Warnecke G. Über das homogene Dirichlet-Problem bei nicht-linearen partiellen Differentialgleichungen vom Typ der Boussinesq-Gleichung, Dissertation, Freie Universität Berlin, 1985. (1985)

Warnecke G. Über das homogene Dirichlet-Problem bei nichtlinearen partiellen Differentialgleichungen vom Typ der Boussinesq-Gleichung, Math. Meth. in the Appl. Sci. 9 (1987), 493-519. (1987) | MR 1200363 | Zbl 0638.35024

Webb J. R. L. Strongly nonlinear elliptic equations, In: Journées d'Analyse non linéaire Lecture Notes in Mathematics 665, Springer Verlag, Berlin, 1977, pp. 242-256. (1977) | MR 0519434

Zabusky N. J. A synergetic approach to problems of nonlinear dispersive wave propagation and interaction, In: Nonlinear partial differential equations (W. F. Ames, Ed.), Academic Press, New York - London, 1967, pp. 223-258. (1967) | Zbl 0183.18104

Zeidler E. Vorlesungen über nichtlineare Funktionalanalysis I - Fixpunktsätze, B. G. Teubner Verlagsgesellschaft, Leipzig, 1976. (1976) | MR 0473927 | Zbl 0326.47053