Nonexistence of classical solutions of the Dirichlet problem for fully nonlinear elliptic equations

N. Kutev

Archivum Mathematicum (1991)

  • Volume: 027, Issue: 1-2, page 31-42
  • ISSN: 0044-8753

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Kutev, N.. "Nonexistence of classical solutions of the Dirichlet problem for fully nonlinear elliptic equations." Archivum Mathematicum 027.1-2 (1991): 31-42. <http://eudml.org/doc/18312>.

@article{Kutev1991,
author = {Kutev, N.},
journal = {Archivum Mathematicum},
keywords = {Monge-Ampère type equations; comparison principle; existence; fully nonlinear, nonuniformly elliptic equations},
language = {eng},
number = {1-2},
pages = {31-42},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Nonexistence of classical solutions of the Dirichlet problem for fully nonlinear elliptic equations},
url = {http://eudml.org/doc/18312},
volume = {027},
year = {1991},
}

TY - JOUR
AU - Kutev, N.
TI - Nonexistence of classical solutions of the Dirichlet problem for fully nonlinear elliptic equations
JO - Archivum Mathematicum
PY - 1991
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 027
IS - 1-2
SP - 31
EP - 42
LA - eng
KW - Monge-Ampère type equations; comparison principle; existence; fully nonlinear, nonuniformly elliptic equations
UR - http://eudml.org/doc/18312
ER -

References

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  1. Bernstein S., Conditions necessаires et suffisаntes pour lа possibilite du probleme de Dirichlet, C. R. Acad. Sci. Paris, 150, (1910), 514-515. (1910) 
  2. Bernstein S., Sur les equаtions du cаlcul des vаriаtions, Ann. Ѕci. Ecole Norm. Ѕup., 29, (1912), 431-485. (1912) MR1509153
  3. Evans L. C., Clаssicаl solutions of fully, nonlineаr convex, second order elliptic equаtions, Comm. Pure Appl. Math. 25, (1982), 333-363. (1982) MR0649348
  4. Gilbarg D., Trudinger N. S., Elliptic pаrtiаl differentiаl equаtions of second order, Ѕpringer Verlag, New York, 1983. (1983) MR0737190
  5. Ivanov A. V., Quаsilineаr degerаte аnd nonuniformly elliptic аnd pаrаbolic equаtions of second order, Trudy Mat. Inst. Ѕteklov (in Russian). 
  6. Krylov N. V., Ѕafonof M. V., Certаin properties of solutions of pаrаbolic equаtions with meаsurаble coefficients, Izvestia Acad. Nauk ЅЅЅR, 40, (1980), 161-175. (1980) 
  7. Krylov N. V., On degenerаte nonlineаr elliptic equаtions I, Mat. Ѕb. 120 (162), (1983) 311-330, II. Mat. Ѕb. 121 (163), (1983), 211-232. (1983) 
  8. Kutev N., Grаdient estimаtes for equаtion of Monge-Ampere type, to appear. 
  9. Kutev N., Existence аnd nonexistence of clаssicаl solutions of the Dirichlet problem for а clаss off ully nonlineаry nonuniformly elliptic equаtions, to appear. 
  10. Ladyzhenskaya O. A., Uraľtseva N. N., Lineаr аnd quasilineаr elliptic equаtions, Acad. Press, New York, 1968. (1968) 
  11. Ѕeгrin J., The problem of Dirichlet for quаsilineаr elliptic differentiаl equаtions with mаny independent vаriаbles, Philos. Tгans. Roy. Ѕoc., London, Ѕer. A 264, (1969), 413-496. (1969) 
  12. Trudinger N. Ѕ., Fully nonlineаr, uniformly elliptic equаtions under nаturаl structure conditions, Tгans. Amer. Math. Ѕoc. 287, (2), (1983), 751-769. (1983) MR0701522
  13. Tгudinger N. Ѕ., Urbas J. I. E., The Dirichlet problem for the equаtion of prescribed Gаus curvаture, Bull. Austral. Math. Ѕoc. 28, (1983), 217-231. (1983) MR0729009

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