On elliptic partial differential equations

L. Nirenberg

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1959)

  • Volume: 13, Issue: 2, page 115-162
  • ISSN: 0391-173X

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Nirenberg, L.. "On elliptic partial differential equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 13.2 (1959): 115-162. <http://eudml.org/doc/83226>.

@article{Nirenberg1959,
author = {Nirenberg, L.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {partial differential equations},
language = {eng},
number = {2},
pages = {115-162},
publisher = {Scuola normale superiore},
title = {On elliptic partial differential equations},
url = {http://eudml.org/doc/83226},
volume = {13},
year = {1959},
}

TY - JOUR
AU - Nirenberg, L.
TI - On elliptic partial differential equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1959
PB - Scuola normale superiore
VL - 13
IS - 2
SP - 115
EP - 162
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/83226
ER -

References

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  1. [1] H. Lewy, An example of a smooth linear partial differential equation without solution. Annals of Math.66 (1957) p. 155-158. Zbl0078.08104MR88629
  2. [2] L. Ehrenpreis, Solutions of some problems of division I, II. American Journal of Math76 (1954) p. 883-903, 77 (1955) p. 286-292. The division problem for distributions. Proc. Nat. Acad. Sci.41-10 (1955) p. 756-758. Zbl0056.10601
  3. [3] L. Hörmander, On the theory of general partial differential operators. Acta Math.94 (1955) p. 160-248. Zbl0067.32201MR76151
  4. [4] B. Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolutions. Annales de L'Inst. Fourier6 (1955 -6) p. 271-355. Zbl0071.09002MR86990
  5. [5] F. Trêves, Solutions élémentaire d'équations aux dérivées partielles dépendent d'un paramètre, C. R. Acad. Sci. Paris242 (1956) p. 1250-1252. Zbl0071.09001MR88631
  6. [6] L. Hörmander, Local and global properties of fundamental solutions. Math. Scandinavica5 (1957) p. 27-39. On the division of distributions by polynomials. Arkiv. för Mat.3 No. 53 (1958) p. 555-568. MR93636
  7. [7] F. John, Plane waves and spherical means applied to partial differential equations. Interscionce, New York, 1955. Zbl0067.32101MR75429
  8. [8] N. Du Plessis, Some theorema about the Riesz fractional integral. Trans. Amer. Math. Soc.80 (1955) p. 124-134. Zbl0067.28101MR86938
  9. [9] L. Nirenberg, Remarks on strongly elliptic partial differential equations. Comm. Pure Appl. Math.8 (1955) p. 649-675. Zbl0067.07602MR75415
  10. [10] L. Bers, L. Nirenberg, (a) On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications. (b) On linear and nonlinear elliptic boundary value problems in the plane. Atti de Convegno Inter, sul. Equazioni alle derivate Parziali, Trieste, 1954 (published 1955). 
  11. [11] De Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari. Mem. della Accad. delle Scienze di Torino. Ser. 3, Vol. 3 (1957) p. 25-43. Zbl0084.31901MR93649
  12. [12] J. Nash, Cantinuity of solutions of parabolic and elliptic equations. Amer. Journ. Math.80 (1958) p. 931-954 Zbl0096.06902MR100158
  13. [13] N. Aronszajn, On coercive integro differential quadratic forms. Conference on Partial Differential Equations, University of Kansas, 1954, Technical Report No. 14, p. 94-106. Zbl0067.32702
  14. [14] S. Agmon, A. Douglis, I.,. NirenbergEstimates near the boundary for solutions of elliptic partial differeratial equations satisfying general boundary conditions I. To appear in Comm. Pure Appl. Math. Zbl0093.10401MR125307
  15. [15] M. Schechter, Integral inequalities for partial differential operators and functions satisfying general boundary conditions, To appear in Comm. Pure Appl. Math. Vol. 12, No. 1 (1959). Zbl0093.29401MR141879
  16. [16] S. Agmon, The coerciveness problem for integro differential forms, Journal d'Analyse Math.6 (1958) p. 184-223. Zbl0119.32302MR132912
  17. [17] L. Hörmander, On the interior regularity of the solutions of partial differential equations. Comm. Pure Appl. Math.11 (1958) p. 197-218. Zbl0081.31501MR106330
  18. [18] B. Malgrange, Sur une classe d'opérateurs différentiels hypoelliptiques. Bull. Soc. Math. France.85, 3 (1957) p. 283-306. Zbl0082.09303MR106329
  19. [19] P.D. Lax, On Cauchy's problem for hyperbolic equations and the differentiability of solutions of elliptic equations. Comm. Pure Appl. Math.8 (1955) p. 615633. Zbl0067.07502MR78558
  20. [20] L. Bers, Elliptic partial differential equations. Lecture notes of the Seminar in Applied Mathematics, University of Colorado, June 1957. 
  21. [21] L. Schwartz, Ecuaciones diferenciales parciales elipticas, Lectures at Bogota Colombia, 1956. MR369893
  22. [22] L. Hörmander, On the regularity of the solutions of boundary problems. Acta Math99 (1958) p. 225-264. Zbl0083.09201MR131655
  23. [23] C. Miranda, Teorema del massimo modulo e teorema di esistenza e di unicità per il problema di Dirichlet relativo alle equazioni ellittiche in due variabili. Annali di Mat. Pura ed Appl. Ser. 4, Vol. 46 (1958) p. 265-312. Zbl0093.29403MR124615
  24. [24] A.P. Calderon, A. Zygmund, On singular integrals, Amer. Journal Math.79 (1956) p. 289-309. Zbl0072.11501MR84633
  25. [25] S. Agmon, Multiple layer potentials and the Dirichlet problem for higher order elliptic equations in the plane I. Comm. Pure Appl. Math.10 (1957) p. 179-239. Zbl0081.09801MR106323
  26. [A] C. Miranda, Equazioni alle derivate parziali di tipo ellittico, Springer, Berlin1955. Zbl0065.08503MR87853
  27. [B] Transactions of the Symposium on Partial Differential Equations. Berkeley California, 1955, published in Comm. Pure Appl. Math., Vol. 9, No. 3 (1956). 
  28. [C] E. Magenes, G. Stampacchia, I problemi al contorno per le equazioni differenziali lineari di tipo ellittico. Annali della Scuola Norm, Sup. di Pisa Ser. 3, Vol. 12, Fasc. 3 (1958) p. 297-358. Zbl0082.09601MR123818

Citations in EuDML Documents

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  1. A. Pełczyński, M. Wojciechowski, Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm
  2. Charles S. Kahane, On the asymptotic behavior of solutions of parabolic equations
  3. Robert A. Adams, Anisotropic Sobolev inequalities
  4. Rodolfo Salvi, On the existence of weak solutions of a nonlinear mixed problem for nonhomogeneous fluids in a time dependent domain
  5. Jishan Fan, Xuanji Jia, Yong Zhou, A logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain
  6. Vladimir G. Maz'ya, Tatjana Olegovna Shaposhnikova, On pointwise interpolation inequalities for derivatives
  7. L. Caffarelli, R. Kohn, L. Nirenberg, First order interpolation inequalities with weights
  8. Renato Manfrin, A remark on global smooth solutions for quasilinear wave equations
  9. H. Beirão Da Veiga, Singular limits in fluidynamics
  10. Ryo Kobayashi, Masakazu Yamamoto, Shuichi Kawashima, Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space

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