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On the dominance of partial differential operators. II. (English) Zbl 0125.05903

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[1] S. Agmon , The coerciveness problem for integro-differential forms Journal D’Analyse Mathematique , vol. 6 ( 1958 ), pp. 183 - 223 . MR 132912 | Zbl 0119.32302 · Zbl 0119.32302 · doi:10.1007/BF02790236
[2] S. Agmon , A. Douglis , and L. Nirenberg , Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I , Communications on Pure and Applied Mathematics , vol. 12 ( 1959 ), pp. 623 - 727 . MR 125307 | Zbl 0093.10401 · Zbl 0093.10401 · doi:10.1002/cpa.3160120405
[3] F.E. Browder , Estimates and existence theorems for elliptic boundary value problems , Proceedings of the National Academy of Sciences , U.S.A ., vol. 45 ( 1959 ), pp. 365 - 372 . MR 132913 | Zbl 0093.29402 · Zbl 0093.29402 · doi:10.1073/pnas.45.3.365
[4] G. Ehrling , On a type of eigenvalue problems for certain elliptic differential operators , Mathematica Scandinavica , vol. 2 ( 1954 ), pp. 267 - 285 . MR 67311 | Zbl 0056.32304 · Zbl 0056.32304 · eudml:165550
[5] K.O. Friedrichs , The identity of weak and strong extensions of differential operators , Transactions of the American Mathematical Society , vol. 55 ( 1944 ), pp. 132 - 151 . MR 9701 | Zbl 0061.26201 · Zbl 0061.26201 · doi:10.2307/1990143
[6] L. Hörmander , On the theory of general partial differential operators , Acta Mathematica , vol. 94 ( 1955 ), pp. 161 - 248 . MR 76151 | Zbl 0067.32201 · Zbl 0067.32201 · doi:10.1007/BF02392492
[7] L. Hörmander , On the regularity of solutions of boundary problems , ibid ., vol. 99 ( 1958 ), pp. 225 - 264 . MR 131655 | Zbl 0083.09201 · Zbl 0083.09201 · doi:10.1007/BF02392427
[8] L. Hörmander , On interior regularity of the solutions of partial differential equations , Communications on Pure and Applied Mathematics , vol. 11 ( 1958 ), pp. 197 - 218 . MR 106330 | Zbl 0081.31501 · Zbl 0081.31501 · doi:10.1002/cpa.3160110205
[9] J.L. Lions and E. Magenes , Problemi ai limiti non omogenei I , Annali della Scnola Normale Superiore di Pisa Scienze Fisiche e Matematiche , Serie 3 , vol 14 ( 1960 ), pp. 269 - 308 . Numdam | MR 133583 | Zbl 0095.30303 · Zbl 0095.30303 · numdam:ASNSP_1960_3_14_3_269_0 · eudml:83249
[10] Ya B. Lopatinski , Reducing boundary problems for differential equations of elliptic type to regular integral equations , Ukrainskiĭ Matematicĕskiĭ Žurnal , vol. 5 ( 1953 ), pp. 123 - 151 . (Russian) MR 73828 | Zbl 0206.40402 · Zbl 0206.40402
[11] L. Nirenberg , Remarks on strongly elliptic partial differential equations , Communications on Pure and Applied Mathematics , vol. 8 ( 1955 ), pp. 648 - 674 . MR 75415 | Zbl 0067.07602 · Zbl 0067.07602 · doi:10.1002/cpa.3160080414
[12] R.E.A.C. Paley and N. Wiener , Fourier Transforms in the Complex Domain , Colloquium Publications , vol. 19 , The American Mathematical Society , New York , 1934 . MR 1451142 | Zbl 0011.01601 · Zbl 0011.01601
[13] J. Peetre , On estimating the solutions of hypoelliptic differential equations near the plane boundary , Mathematica Scandinavica , vol. 9 ( 1961 ), pp. 337 - 351 . MR 146517 | Zbl 0113.30601 · Zbl 0113.30601 · eudml:165779
[14] J. Peetre , Another approach to elliptic boundary problems , Communications on Pure and Applied Mathematics , vol. 14 ( 1961 ), pp. 711 - 731 . MR 171069 | Zbl 0104.07303 · Zbl 0104.07303 · doi:10.1002/cpa.3160140404
[15] M. Schechter , On estimating elliptic partial differential operators in the L2 norm , American Journal of Mathematics , vol. 79 ( 1957 ), pp. 431 - 443 . MR 88648 | Zbl 0079.11701 · Zbl 0079.11701 · doi:10.2307/2372690
[16] M. Schechter , Integral inequalities for partial differential operators and functions satisfying general boundary conditions , Communications on Pnre and Applied Mathematics , vol. 12 ( 1959 ), pp. 37 - 66 . MR 141879 | Zbl 0093.29401 · Zbl 0093.29401 · doi:10.1002/cpa.3160120104
[17] M. Schechter , General boundary value problems for elliptic partial differential equations , ibid. , vol. 12 ( 1959 ), pp. 457 - 486 . MR 125323 | Zbl 0087.30204 · Zbl 0087.30204 · doi:10.1002/cpa.3160120305
[18] M. Schechter , Remarks on elliptic boundary value problems . ibid. , vol. 12 ( 1959 ), pp. 561 - 578 . MR 125330 | Zbl 0095.07902 · Zbl 0095.07902 · doi:10.1002/cpa.3160120402
[19] M. Schechter , On the dominance of partial differential operators , Transactions of the American Mathematical Society , vol. 107 ( 1963 ), pp. 237 - 260 . MR 188613 | Zbl 0118.31002 · Zbl 0118.31002 · doi:10.2307/1993892
[20] L. Schwartz , Theorie des distributions I, II , Hermann , Paris , 1950 - 1951 . Zbl 0042.11405 · Zbl 0042.11405
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