An L p -estimate for the gradient of solutions of second order elliptic divergence equations

Norman G. Meyers

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1963)

  • Volume: 17, Issue: 3, page 189-206
  • ISSN: 0391-173X

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Meyers, Norman G.. "An $L^p$-estimate for the gradient of solutions of second order elliptic divergence equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.3 (1963): 189-206. <http://eudml.org/doc/83302>.

@article{Meyers1963,
author = {Meyers, Norman G.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {partial differential equations},
language = {eng},
number = {3},
pages = {189-206},
publisher = {Scuola normale superiore},
title = {An $L^p$-estimate for the gradient of solutions of second order elliptic divergence equations},
url = {http://eudml.org/doc/83302},
volume = {17},
year = {1963},
}

TY - JOUR
AU - Meyers, Norman G.
TI - An $L^p$-estimate for the gradient of solutions of second order elliptic divergence equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1963
PB - Scuola normale superiore
VL - 17
IS - 3
SP - 189
EP - 206
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/83302
ER -

References

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  1. [1] Agmon, S. Douglis, A. and Nirenberg, L.Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Com. Pure Appl. Math.12, pp. 623-727 (1959). Zbl0093.10401MR125307
  2. u [2] Boyarskii, B.V.Homeomorphic solutions of Beltrami systems, Dokl. Akad. Nauk. SSSR.(N. S.) 102, (1955) (Russian). MR71620
  3. u [3] Boyarskii, B.V.Generalized solutions of a system of differential equations of the first order of elliptic type with discontinuous coefficients, Mat. Sbornik N. S.43, pp. 451-503 (1957) (Russian). MR106324
  4. [4] Calderon, A.P. and Zygmund, A.On the existence of certain singular integrals, Acta. Math., 88, pp. 85-139 (1952). Zbl0047.10201MR52553
  5. [5] De Giorgi, E.Sulla differentiabilità e l'analiticitá delle extremali degli integrali multipli regolari, Mem. Accad. Sci. Torino, S. III, Parte I, pp. 25-43 (1957) Zbl0084.31901
  6. [6] Dunford, N. and Schwartz, J.Linear Operators Part I, Interscience (New York) (1958). Zbl0084.10402
  7. [7] Finn, R. and Serrin, J.On the Hölder continuity of quasi-conformal and elliptic mappings, Trans. Amer. Math. Soc.89, pp. 1-15 (1958). Zbl0082.29401MR97626
  8. [8] Moser, J.A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations. Comm. Pure Appl. Math.13, pp 457-468 (1960). Zbl0111.09301MR170091
  9. [9] Vekua, I.N.The problem of reduction to canonical form of differential forms of elliptic type and generalized Cauchy Riemann systems, Dokl. Acad. Nauk.100, pp. 197-200 (1955) (Russian). Zbl0068.06401MR70011

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  5. Abdelmounim Belahmidi, Antonin Chambolle, Time-delay regularization of anisotropic diffusion and image processing
  6. Robert Lipton, Tadele Mengesha, Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization
  7. Gérard Gagneux, Roland Masson, Anne Plouvier-Debaigt, Guy Vallet, Sylvie Wolf, Vertical compaction in a faulted sedimentary basin
  8. Luca Rondi, Fadil Santosa, Enhanced electrical impedance tomography via the Mumford–Shah functional
  9. S. Wardi, A convergence result for an iterative method for the equations of a stationary quasi-newtonian flow with temperature dependent viscosity
  10. Tullio Valent, Giuseppe Zampieri, Sulla differenziabilità di un operatore legato a una classe di sistemi differenziali quasi-lineari

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