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Mixed boundary value problems for elliptic equations in the plane. The \(L^ p\) theory. (English) Zbl 0117.07002

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[1] 1 Agmon , S. The LP approach to the Dirichlet problem , Annali di Pisa , 13 ( 1959 ), 49 - 92 . Numdam | MR 125306 | Zbl 0108.10203 · Zbl 0108.10203 · numdam:ASNSP_1959_3_13_4_405_0
[2] 2 Agmon , S. , Dougli , A. and Nirenberg , L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general bonudary conditions . Comm. Pure Appl. Math. 12 ( 1959 ), 623 - 727 . MR 125307 | Zbl 0093.10401 · Zbl 0093.10401 · doi:10.1002/cpa.3160120405
[3] 3 Aronszajn , N. and Smith , K.T. Theory of Bessel potentials (I) . Annales Inst. Fourier 11 ( 1961 ), 385 - 475 . (II-to appear). Numdam | MR 143935 | Zbl 0102.32401 · Zbl 0102.32401 · doi:10.5802/aif.116 · numdam:AIF_1961__11__385_0 · eudml:73778
[4] 4 Browder , F.E. Estimates and existence theorems for elliptic boundary value problems Proo. Nat. Acad. Sci U. S. A. 45 ( 1959 ), 365 - 372 . MR 132913 | Zbl 0093.29402 · Zbl 0093.29402 · doi:10.1073/pnas.45.3.365
[5] 5 Browder , F.E. A priori estimates for solutions of elliptic boundary value problems (I) (II) . Konink. Ned. Akad. Van Wetenschap 22 ( 1960 ), 145 - 159 , 160 - 169 . MR 123819 | Zbl 0096.30202 · Zbl 0096.30202
[6] 6 Calderon , A.P. and Zygmund , A. On singular integrals . Amer J. Math. 78 ( 1956 ), 289 - 309 . MR 84633 | Zbl 0072.11501 · Zbl 0072.11501 · doi:10.2307/2372517
[7] 7 Lions , J.L. Théorèmes de traces et d’interpolation (I) . Annali di Pisa 13 ( 1959 ), 389 - 403 . Numdam | MR 119092 | Zbl 0097.09502 · Zbl 0097.09502 · numdam:ASNSP_1959_3_13_4_389_0 · eudml:83234
[8] 8 Lions , J.L. Equations differentielles operationelles et problèmes aux limites , Springer Verlag , Berlin , Göttingen , Heidelberg , 1961 . MR 153974 | Zbl 0098.31101 · Zbl 0098.31101
[9] 9 Lions , J.L. and Magenes , E. Problemi ai limiti non omogenei (III) Annali di Pisa 15 ( 1961 ), 39 - 101 . Numdam | MR 146526 · numdam:ASNSP_1961_3_15_1-2_41_0
[10] 10 Lions , J.L. Problemes aux limites non homogènes (IV) Annali di Pisa 15 ( 1961 ), 311 - 326 . Numdam | MR 140938 | Zbl 0115.31302 · Zbl 0115.31302 · numdam:ASNSP_1961_3_15_4_311_0 · eudml:83269
[11] 11 Lions , J.L. and Magenes , E. Problemi ai limiti non omogenei (V) . Annali di Pisa 16 ( 1962 ), 1 - 44 . Numdam | MR 146527 | Zbl 0115.31401 · Zbl 0115.31401 · numdam:ASNSP_1962_3_16_1_1_0 · eudml:83273
[12] 12 Muskhelishvili , W.I. Singular integral equation (English translation) P. Nordhoff N. V , Groningen , 1953 . Zbl 0051.33203 · Zbl 0051.33203
[13] 13 Nikolski , M. On the imbedding, continuation and approximation theorems for differentiable functions in many variables . Usp. Mat. Nauk. 16 , 5 ( 1961 ), 63 - 114 . MR 149267 | Zbl 0117.29101 · Zbl 0117.29101 · doi:10.1070/rm1961v016n05ABEH004113
[14] 14 Peetre , J. Another approach to elliptic boundary problems . Comm. Pure Appl. Math. 14 ( 1961 ) 711 - 731 . MR 171069 | Zbl 0104.07303 · Zbl 0104.07303 · doi:10.1002/cpa.3160140404
[15] 15 Peetre , J. Mixed problems for higher order elliptic equations in two variables (I) . Annali di Pisa 15 ( 1961 ), 337 - 353 . Numdam | MR 140826 | Zbl 0108.28802 · Zbl 0108.28802 · numdam:ASNSP_1961_3_15_4_337_0 · eudml:83271
[16] 16 Schechter , M. General boundary value problems for elliptic partial differential equations . Comm. Pure App. Math. 12 ( 1959 ), 451 - 485 . MR 125323 | Zbl 0087.30204 · Zbl 0087.30204 · doi:10.1002/cpa.3160120305
[17] 17 Schechter , M. Mixed problems for higher order elliptic equations . Comm. Pure App. Math. 13 ( 1960 ), 407 - 425 . MR 125331 | Zbl 0095.08002 · Zbl 0095.08002 · doi:10.1002/cpa.3160130306
[18] 18 Schechter , M. Some LP estimates for partial differential equations . Bull. Amer. Math. Soo. 68 ( 1962 ), 470 - 474 . Article | MR 139854 | Zbl 0113.30602 · Zbl 0113.30602 · doi:10.1090/S0002-9904-1962-10779-4 · minidml.mathdoc.fr
[19] 19 Shamir , E. Évaluations dans Ws,p pour des problèmes aux limites elliptiques mixtes dans le plan . C. P. Acad. Sci. Paris 254 ( 1962 ), 3621 - 3623 . MR 139841 | Zbl 0123.07402 · Zbl 0123.07402
[20] 20 Uspenski , S.V. An imbedding theorem for Sobolev classes of fractional order . Dok Akad. Nauk S. S. S. R , 130 ( 1960 ), 992 - 993 . MR 124731 | Zbl 0103.08205 · Zbl 0103.08205
[21] 21 Uspenski , S.V. Properties of the classes Wr,p of fractional derivates on differentiable manifolds , Dok. Akad. Nauk S. S. S. R. 132 ( 1960 ), 60 - 62 . MR 124732 | Zbl 0103.08204 · Zbl 0103.08204
[22] 22 Shamir , E. Reduced Hilbert transforms and singular integral equations . The appear in J. D’analyse Math. , ( 1964 ). MR 165328 | Zbl 0173.14502 · Zbl 0173.14502 · doi:10.1007/BF02807437
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