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1998 | 69 | 2 | 129-154
Tytuł artykułu

Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider generalized solutions to the Dirichlet problem for linear elliptic second order equations in a domain bounded by a Dini-Lyapunov surface and containing a conical point. For such solutions we derive Dini estimates for the first order generalized derivatives.
Rocznik
Tom
69
Numer
2
Strony
129-154
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-06-12
poprawiono
1997-10-15
poprawiono
1997-12-15
Twórcy
  • Department of Applied Mathematics, Olsztyn University of Agriculture and Technology, 10-957 Olsztyn-Kortowo, Poland
Bibliografia
  • [1] A. Azzam and V. Kondrat'ev, Schauder-type estimates of solutions of second order elliptic systems in divergence form in non-regular domains, Comm. Partial Differential Equations 16 (1991), 1857-1878.
  • [2] M. Borsuk, Best-possible estimates of solutions of the Dirichlet problem for linear elliptic nondivergence equations of second order in a neighbourhood of a conical point of the boundary, Math. USSR-Sb. 74 (1993), 185-201.
  • [3] C. Burch, The Dini condition and regularity of weak solutions of elliptic equations, J. Differential Equations 30 (1978), 308-323.
  • [4] S. Eĭdel'man and M. Matiĭchuk, The Cauchy problem for parabolic systems with coefficients having low smoothness, Ukrain. Mat. Zh. 22 (1970), 22-36 (in Russian).
  • [5] D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1983.
  • [6] V. Kondrat'ev, I. Kopachek and O. Oleĭnik, On the best Hölder exponents for generalized solutions of the Dirichlet problem for a second-order elliptic equation, Mat. Sb. 131 (1986), 113-125 (in Russian); English transl.: Math. USSR-Sb. 59 (1988).
  • [7] G. Lieberman, The Dirichlet problem for quasilinear elliptic equations with continuously differentiable boundary data, Comm. Partial Differential Equations 11 (1986), 167-229.
  • [8] E. Sperner, Schauder's existence theorem for α-Dini continuous data, Ark. Mat. 19 (1981), 193-216.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv69z2p129bwm
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