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Regularity theorems for solutions of partial differential equations for quasiconformal mappings in several dimensions

Seria
Rozprawy Matematyczne tom/nr w serii: 198 wydano: 1982
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Abstrakty
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CONTENTS

Preliminaries........................................................................................................ 5
1. Auxiliary results......................................................................................................... 13
2. The second order equations.................................................................................. 14
3. Some properties of Sobolev and Besov spaces................................................ 20
4. Classes $Λ^α(G, H)$, 0 < a ≤ 1............................................................................ 21
5. The case of Lipschitz characteristics................................................................... 26
6. Existence of second partial derivatives and its consequences...................... 29
7. Local boundedness of the Jacobian.................................................................... 33
8. Smoothness.............................................................................................................. 41
References.................................................................................................................... 44
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 198
Liczba stron
45
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXCVIII
Daty
wydano
1982
Twórcy
Bibliografia
  • [1] L. Ahlfors, Deformation of quasiconformal maps in several variables, contributions to Analysis, 1974.
  • [2] O. V. Besov, W. P. Ilin, S. M. Nikolski, The integral expressions of functions and embedding theorems, Nauka, Moskva 1975 (Russian).
  • [3] B. Bojarski, Generalized solutions of first order elliptic equations with discontinuous coefficients, Mat. Sb. 43 (85) (1957), pp. 451-503 (Russian).
  • [4] B. Bojarski, Quasiconformal mappings and general structural properties of systems of non-linear equations elliptic in the sense of Lavren'ev, Symp. Math. 16 (1976), pp. 485-488.
  • [5] B. Bojarski and T. Iwaniec, Topics in quasiconformal theory in several variables, Proceedings of the First Finnish-Polish Summer School in Complex Analysis, Part II, Łódź 1977.
  • [6] B. Bojarski and T. Iwaniec, Quasiconformal mappings and non-linear elliptic systems in two variables I, II, Bull. Acad. Polon. Sci, pp. 473-484.
  • [7] A. Elcart and G. Meyers, Some results on regularity for solutions of non-linear elliptic systems and quasiregular functions, Duke Math. J. 42 (1975), pp. 121-136.
  • [8] F. W. Gehring, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103, 3 (1962), pp. 353-393.
  • [9] F. W. Gehring, $L^p$-integrability of the partial derivatives of a quasiconformal mappings, Acta Math. 130 (1973), pp. 265-277.
  • [10] V. M. Goldstein, On the behaviour of mappings with bounded distortion, for the coefficient of distortion close to the unity, Inst. Mat. Sib. Otdel. AN SSSR, preprint, Novosibirsk 1970, pp. 1-16 (Russian).
  • [11] T. Iwaniec, Quasiconformal mapping problem for general nonlinear systems of partial differential equations, Symp. Math. 18 (1976), pp. 501-517.
  • [12] T. Iwaniec, Regularity problem for systems of partial differential equations admitting quasiconformal mappings in space, to appear in the volume dedicated to the memory of I. N. Vekua, Tbilisi 1978.
  • [13] O. A. Ladyzenskaya and N. Uraltseva, Linear and quasilinear equations of elliptic type, Nauka, Moskva 1973 (Russian).
  • [14] M. A. Lavrentiev, A general problem of the theory of quasiconformal representations of plane regions, Mat. Sb. 21 (1947), pp. 285-320.
  • [15] M. A. Lavrentiev, The fundamental theorem of the theory of quasiconformal mappings of two-dimensional domain, Izv. Acad. Sci USSR 12 (1948), pp. 512-554.
  • [16] O. Martio, A capacity inequality for quasiregular mappings, Ann. Acad. Sci. Fenn. AI 474 (1970), pp. 1-18.
  • [17] Ch. Morrey, Multiple integrals in the calculus of variations, Springer-Verlag, Berlin-Heidelberg-New York 1966.
  • [18] S. M. Nikolski, Approximation of functions of several variables and embedding theorems, Nauka, Moskva 1969 (Russian).
  • [19] J. G. Rešetniak, Evaluations of the module of some mappings, Sibirsk. Mat. Ž. 7 (1966), pp. 1106-1114.
  • [20] J. G. Rešetniak, Liouvilles theorem on conformal mappings with minimal hypotheses of regularity, ibid. 8 (1967), pp. 835-840.
  • [21] J. G. Rešetniak, Mappings with bounded distortion as extrema of the integrals of Dirichlet type, ibid. 9 (1968), pp. 625-666.
  • [22] B. V. Šabat, On generalized solutions of a system of partial differential equations, Mat. Sb. 17 (59) (1945), pp. 193-209, (Russian).
  • [23] S. Saks, Theory of integral, Hafner Publishing Company, New York 1937.
  • [24] J. Serrin, Local behaviour of solutions of quasilinear equations. Acta Math. (1964), pp. 247-302.
  • [25] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton, New Jersey 1970.
  • [26] B. Bojarski and T. Iwaniec, Another approach to Liouville theorem, to appear in Mathematische Nachrichten, 1982.
Języki publikacji
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Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-931a70e0-c97a-4f48-bdbb-c9d5a408ca3a
Identyfikatory
ISBN
83-01-01614-0
ISSN
0012-3862
Kolekcja
DML-PL
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