no. 4
The L p approach to the Dirichlet problem. Part I : regularity theorems
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 13 (1959) no. 4, pp. 405-448. 
@article{ASNSP_1959_3_13_4_405_0,
     author = {Agmon, Shmuel},
     title = {The $L_p$ approach to the {Dirichlet} problem. {Part} {I} : regularity theorems},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {405--448},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 13},
     number = {4},
     year = {1959},
     zbl = {0093.10601},
     mrnumber = {125306},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1959_3_13_4_405_0/}
}
TY  - JOUR
AU  - Agmon, Shmuel
TI  - The $L_p$ approach to the Dirichlet problem. Part I : regularity theorems
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1959
DA  - 1959///
SP  - 405
EP  - 448
VL  - Ser. 3, 13
IS  - 4
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1959_3_13_4_405_0/
UR  - https://zbmath.org/?q=an%3A0093.10601
UR  - https://www.ams.org/mathscinet-getitem?mr=125306
LA  - en
ID  - ASNSP_1959_3_13_4_405_0
ER  - 
Agmon, Shmuel. The $L_p$ approach to the Dirichlet problem. Part I : regularity theorems. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 13 (1959) no. 4, pp. 405-448. http://archive.numdam.org/item/ASNSP_1959_3_13_4_405_0/

[1] Agmon. S., Multiple layer potentials and the Diriohlet problem for higher order elliptic equations in the plane I, Comm. Pure Appl. Math., Vol. 10, 1957, pp. 179-240. | MR 106323 | Zbl 0081.09801

[2] Agmon, S., The coerciveness problem for integro-differential forms, J. d'Analyse Math., Vol. 6, 1958, pp. 183-223. | MR 132912 | Zbl 0119.32302

[3] Agmon, S., Douglis, A. and Nirenberg, L., Dstimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math., Vol. 12, No. 4, 1959. | MR 125307 | Zbl 0093.10401

[4] Aronszajn, N., On Coercive integro-differential quadratic forms, Conference of Partial Differential Equations, University of Kansas, Technical Report No. 14, pp. 94-106. | Zbl 0067.32702

[5] Babich, V.M., On a problem of extension of functions, Uspehi Mat. Nauk. N. S., Vol. 8, no. 2 (54), 1953, pp. 111-113 (in Russian). | MR 56675 | Zbl 0050.06201

[6] Browder F.E., Strongly etliptic systems of differential equations, Ann. Math. Study No. 33. Princeton University Press, 1954, pp. 15-51. | MR 67306 | Zbl 0057.32901

[7] Browder, F.E., On the regularity properties of solutions of elliptic partial differential equations, Comm. Pure Appl. Math., Vol. 9, 1956, pp. 351-361. | MR 90740 | Zbl 0070.09601

[8] Calderon A.P. and Zigmund, A., On singular integrals, Amer. J. Math., Vol. 78, 1956, pp. 289-309. | MR 84633 | Zbl 0072.11501

[9] Deny J. and Lions J.L., Les espace de Beppo Levi, Ann. Inst. Fourier, Vol. 5, 1953-54, pp. 305-370. | Numdam | Zbl 0065.09903

[10] Fichera, G., Alcuni recenti sviluppi della teoria dei problemi al contorno per le equazioni alle derivate parziali lineari, Atti Cong. Int. Equaz. Lin. der. parz. di Trieste, 1954, pp. 174-227. | MR 74665 | Zbl 0068.31101

[11] Friedrichs, K.O., The identity of weak and strong extensions of differential operators, Trans. Amer. Math. Soc., Vol. 55, No. 1, 1944, pp. 132-151. | MR 9701 | Zbl 0061.26201

[12] Friedrichs, K.O., On the differentiability of solutions of linear elliptic differential equations, Comm. Pure Appl. Math., Vol. 6, 1953, pp. 299-326. | MR 58828 | Zbl 0051.32703

[13] Gagliardo, E., Proprietà di alcune classi di funzioni in più variabili, Ric. di Mat., Vol. 7, 1958, pp. 102-137. | MR 102740 | Zbl 0089.09401

[14] Gårding, L., Dirichlet's problem for linear elliptic partial differential equations, Math. Scand., Vol. 1, 1953, pp. 55-72. | MR 64979 | Zbl 0053.39101

[15] Hörmander, L., Differentiability properties of solutions of systems of differential equations, Ark. for Mat. Vol. 3, 1958, pp. 527-535. | MR 104923 | Zbl 0131.09503

[16] John, F., Plane waves and spherical means applied to partial differential equations, Interscience. New York, 1955. | MR 75429 | Zbl 0067.32101

[17] Koselev, A.I., On boundedness in Lp of derivatives of solutions of elliptic equations and systems, Doklady Akad. Nauk USSR, Vol. 116, 1957, pp. 542-544 (in Russian). | MR 96896 | Zbl 0081.09802

[18] Lions, J.L., Problemès aux limites en theorie des distributions, Acta Math., Vol. 94, 1955, pp. 13-153. | MR 75425 | Zbl 0068.30902

[19] Magenes, E. and Stampacchia, G., I problemi al contorno per le equazioui differenziali di tipo ellittico, Ann. Sc. Norm. Sup. Pisa Vol. 12, 1958, pp. 247-358. | Numdam | MR 123818 | Zbl 0082.09601

[20] Miranda, C., Teorema del massimo modulo e teorema di essistenza e di unicita per il problema di Dirichlet redativo alle equazioni ellittiche in due variabili, Ann. Mat. Pura Appl., Vol. 46, 1958, pp. 265-312. | MR 124615 | Zbl 0093.29403

[21] Morrey, C.B. Functions of several variables and obsolute continuity, Duke Math. J., Vol. 6, 1940, pp. 187-215. | JFM 66.1225.01 | MR 1279 | Zbl 0026.39401

[22] Morrey, C.B., Second order elliptic systems of differential equations, Contributions to the Theory of Partial Differential Equations, Ann. Math. Studies No. 33 Princeton, 1954, pp. 101-159. | MR 68091 | Zbl 0057.08301

[23] Nirenberg, L., Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math., Vol. 8, 1955, pp. 648-674. | MR 75415 | Zbl 0067.07602

[24] Nirenberg, L., Estimates and existence of solutions of elliptic equations, Comm. Pure Appl. Math., Vol. 9, 1956, pp. 509-530. | MR 91402 | Zbl 0070.32301

[25] Schechter, M., Integral inequalities for partial differential operators and functions satisfying general boundary conditions, Comm. Pure Appl. Math., Vol. 12, 1959, pp. 37-66. | MR 141879 | Zbl 0093.29401

[26] Schechter, M., Solution of the Dirichlet problem for systems not necessarily strongly elliptic, Comm. Pure Appl. Math., Vol. 12, 1959, pp. 241-247. | MR 155088 | Zbl 0086.30302

[27] Schechter, M., General boundary value problems for elliptic partial differential equations, Bull. Amer Math. Soc., Vol. 65, 1959, pp. 70-72. | Zbl 0087.30203

[28] Schwartz, L., Théorie des distributions, Hermann, Paris, 1950-51. | MR 209834 | Zbl 0037.07301

[29] Schwartz, L., Su alcuni problemi della teoria delle equazioni differenziali lineari di tipo ellittico, Rend. Sem. Mat. Fis. Milano, Vol. 27, 1958, pp. 211-249. | Zbl 0086.08103

[30] Sobolev S.L., On a theorem of functional analysis, Mat. Sbornik, N. S. 4, 1938, pp. 471-497 (in Russian). | Zbl 0131.11501

[31] Stampacchia, G., Sopra una classe di funzioni in n variabili, Ric. di Mat., Vol. 1, 1951, pp. 27-54. | MR 48551 | Zbl 0049.16802

[32] Vishik, M.I., On strongly elliptic systems of differential equations, Mat. Sbornik, Vol. 29, 1951, pp. 617-676 (in Russian). | MR 49440