Counterexample to the regularity of weak solution of elliptic systems

Jindřich Nečas; Oldřich John; Jana Stará

Commentationes Mathematicae Universitatis Carolinae (1980)

  • Volume: 021, Issue: 1, page 145-154
  • ISSN: 0010-2628

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Nečas, Jindřich, John, Oldřich, and Stará, Jana. "Counterexample to the regularity of weak solution of elliptic systems." Commentationes Mathematicae Universitatis Carolinae 021.1 (1980): 145-154. <http://eudml.org/doc/17022>.

@article{Nečas1980,
author = {Nečas, Jindřich, John, Oldřich, Stará, Jana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {counterexample; regularity of weak solution; elliptic systems},
language = {eng},
number = {1},
pages = {145-154},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Counterexample to the regularity of weak solution of elliptic systems},
url = {http://eudml.org/doc/17022},
volume = {021},
year = {1980},
}

TY - JOUR
AU - Nečas, Jindřich
AU - John, Oldřich
AU - Stará, Jana
TI - Counterexample to the regularity of weak solution of elliptic systems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1980
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 021
IS - 1
SP - 145
EP - 154
LA - eng
KW - counterexample; regularity of weak solution; elliptic systems
UR - http://eudml.org/doc/17022
ER -

References

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  1. De GIORGI E., Sulla differenziabilità e l'analicità delle estremali degli integrali multipli regolari, Mem. Acad. Sci. Torino 3 (1957), 25-43, Matematika 4 (1960), 25-38. (1957) MR0093649
  2. De GIORGI E., Un esempio di estremali discontinue per un problema variazionale di tipo ellittico, Boll. Unione Mat. Italiana 1 (1968), 135-138. (1968) MR0227827
  3. GIUSTI E., MIRANDA M., Un esempio di soluzioni discontinue per un problema di minimo relativo ad un integrále regolare del calcolo delle variazioni, Boll. Unione Mat. Italiana (4) 1 (1968), 219-227. (1968) Zbl0155.44501MR0232265
  4. KOŠELEV A. I., Regularnosť rešenij kvasilinějnych eliptičeskich sistem, Uspechi mat. nauk 23 (1978), 3-49. (1978) MR0510669
  5. LADYŽENSKAJA O. A., URAL'CEVA N. N., Linějnyje i kvasilinějnyje uravněnija eliptičeskogo tipa, Nauka, Moskva 1964. (1964) MR0211073
  6. MORREY Ch. B., Differentiability theorems for weak solutions of nonlinear elliptic differential equations, Bull. Am. Math. Soc. 75 (1969), 684-705. (1969) Zbl0181.38001MR0246182
  7. MORREY Ch. B., Existence and differentiability theorems for the solutions of variational problems for multiple integrals, Bull. Am. Math. Soc. 46 (1940), 439-458. (1940) Zbl0063.04105MR0002473
  8. NASH J., Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1950),931-954. (1950) MR0100158
  9. NEČAS J., Sur la régularité des solutions variationalles des équations elliptiques non-linéaires d’ordre 2 k en deux dimensions, Annali Sc. Norm. Sup. Pisa 21 (1967), 427-457. (1967) MR0226467
  10. NEČAS J., Example of an irregular solution to a nonlinear elliptic system with analytic coefficients and conditions for regularity, Abh. Deutsch. Akad. Wiss. Berlin K1. Math. Phys. Tech., 1977, 1N, 197-206. (1977) MR0509483

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