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The\(L_p\) approach to the Dirichlet problem. (English) Zbl 0093.10601


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[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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · 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 · Zbl 0093.29403
[21] Morrey , C.B. Functions of several variables and obsolute continuity , Duke Math. J. , Vol. 6 , 1940 , pp. 187 - 215 . Article | MR 1279 | Zbl 0026.39401 | JFM 66.1225.01 · 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 · 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 · 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 · 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 · 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 · 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 . Article | Zbl 0087.30203 · Zbl 0087.30203
[28] Schwartz , L. , Théorie des distributions , Hermann , Paris , 1950 - 51 . MR 209834 | Zbl 0037.07301 · 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 · 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 · 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 · 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
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