The Fredholm method in potential theory
HTML articles powered by AMS MathViewer
- by Josef Král
- Trans. Amer. Math. Soc. 125 (1966), 511-547
- DOI: https://doi.org/10.1090/S0002-9947-1966-0209503-0
- PDF | Request permission
References
- M. Brelot, Éléments de la théorie classique du potentiel, “Les Cours de Sorbonne”, vol. 3, Centre de Documentation Universitaire, Paris, 1959 (French). MR 0106366
- M. Brelot and G. Choquet, Espaces et lignes de Green, Ann. Inst. Fourier (Grenoble) 3 (1951), 199–263 (1952) (French). MR 62883, DOI 10.5802/aif.38
- Ju. D. Burago, V. G. Maz′ja, and V. D. Sapožnikova, On the potential of a double layer for non-regular domains, Dokl. Akad. Nauk SSSR 147 (1962), 523–525 (Russian). MR 0145095
- Corneliu Constantinescu and Aurel Cornea, Ideale Ränder Riemannscher Flächen, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 32, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963 (German). MR 0159935, DOI 10.1007/978-3-642-87031-6
- Jacques Deny, Les potentiels d’énergie finie, Acta Math. 82 (1950), 107–183 (French). MR 36371, DOI 10.1007/BF02398276
- Ennio De Giorgi, Su una teoria generale della misura $(r-1)$-dimensionale in uno spazio ad $r$ dimensioni, Ann. Mat. Pura Appl. (4) 36 (1954), 191–213 (Italian). MR 62214, DOI 10.1007/BF02412838
- Ennio De Giorgi, Nuovi teoremi relativi alle misure $(r-1)$-dimensionali in uno spazio ad $r$ dimensioni, Ricerche Mat. 4 (1955), 95–113 (Italian). MR 74499 —, Complementi alla teoria della misura $(n - 1)$-dimensionale in uno spazio $n$-dimensionale, Seminario di Matematica della Scuola Norm. Sup. di Pisa, Anno Accademico, 1960-1961.
- Herbert Federer, The Gauss-Green theorem, Trans. Amer. Math. Soc. 58 (1945), 44–76. MR 13786, DOI 10.1090/S0002-9947-1945-0013786-6
- Herbert Federer, The $(\varphi ,k)$ rectifiable subsets of $n$-space, Trans. Amer. Math. Soc. 62 (1947), 114–192. MR 22594, DOI 10.1090/S0002-9947-1947-0022594-3
- Herbert Federer, A note on the Gauss-Green theorem, Proc. Amer. Math. Soc. 9 (1958), 447–451. MR 95245, DOI 10.1090/S0002-9939-1958-0095245-2
- Herbert Federer and Wendell H. Fleming, Normal and integral currents, Ann. of Math. (2) 72 (1960), 458–520. MR 123260, DOI 10.2307/1970227
- W. H. Fleming, Functions with generalized gradient and generalized surfaces, Ann. Mat. Pura Appl. (4) 44 (1957), 92, 93–103. MR 95923, DOI 10.1007/BF02415193
- Wendell H. Fleming, Functions whose partial derivatives are measures, Illinois J. Math. 4 (1960), 452–478. MR 130338
- W. H. Fleming and L. C. Young, Representations of generalized surfaces as mixtures, Rend. Circ. Mat. Palermo (2) 5 (1956), 117–144. MR 82144, DOI 10.1007/BF02854351
- Josef Král, On the logarithmic potential, Comment. Math. Univ. Carolinae 3 (1962), no. 1, 3–10. MR 159008
- Iosef Kral, On the potential of a double layer in a higher-dimensional space, Dokl. Akad. Nauk SSSR 159 (1964), 1218–1220 (Russian). MR 0176210
- Josef Král, The Fredholm radius of an operator in potential theory, Czechoslovak Math. J. 15(90) (1965), 454–473; ibid. 15 (90), (1965), 565–588 (English, with Russian summary). MR 190363, DOI 10.21136/CMJ.1965.100686
- Klaus Krickeberg, Distributionen, Funktionen beschränkter Variation und Lebesguescher Inhalt nichtparametrischer Flächen, Ann. Mat. Pura Appl. (4) 44 (1957), 92, 105–133 (German). MR 95922, DOI 10.1007/BF02415194
- Fumi-Yuki Maeda, Normal derivatives on an ideal boundary, J. Sci. Hiroshima Univ. Ser. A-I Math. 28 (1964), 113–131. MR 177126
- Jan Mařík, The surface integral, Czechoslovak Math. J. 6(81) (1956), 522–558 (English, with Russian summary). MR 89891, DOI 10.21136/CMJ.1956.100219
- Mario Miranda, Distribuzioni aventi derivate misure insiemi di perimetro localmente finito, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 18 (1964), 27–56 (Italian). MR 165073
- V. G. Maz′ja and V. D. Sapožnikova, Solution of the Dirichlet and Neumann problems for irregular domains by potential-theoretic methods, Dokl. Akad. Nauk SSSR 159 (1964), 1221–1223 (Russian). MR 0180688
- C. Y. Pauc, Functions with generalized gradients in the theory of cell functions, Ann. Mat. Pura Appl. (4) 44 (1957), 92, 135–152. MR 95924, DOI 10.1007/BF02415195 F. Riesz and B. Sz. Nagy, Leçons d’analyse fonctionelle, Akadémiai Kiadó, Budapest, 1952. L. Schwartz, Théorie des distributions. I, II, Actualités Sci. Ind. Nos. 1091, 1122, Hermann, Paris.
- L. C. Young, A theory of boundary values, Proc. London Math. Soc. (3) 14a (1965), 300–314. MR 180891, DOI 10.1112/plms/s3-14A.1.300
Bibliographic Information
- © Copyright 1966 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 125 (1966), 511-547
- MSC: Primary 31.20
- DOI: https://doi.org/10.1090/S0002-9947-1966-0209503-0
- MathSciNet review: 0209503