Аннотация:
Рассматривается задача Дирихле E(uxixj,uxi,u,x)=0 в Ω⊂Rd, u=φ на ∂Ω, для нелинейных эллиптических уравнений, охватывающих уравнения Беллмана с “коэффициентами” из пространства Гёльдера Cα(¯¯¯¯Ω). Доказывается, что если α>0 достаточно мало, то эта задача разрешима в C2+αloc(Ω)∩C(¯¯¯¯Ω). Если, кроме того, ∂Ω∈C2+α и φ∈C2+α(¯¯¯¯Ω), то решение принадлежит C2+α(¯¯¯¯Ω).
Библиография: 18 названий.
Образец цитирования:
М. В. Сафонов, “О классическом решении нелинейных эллиптических уравнений второго порядка”, Изв. АН СССР. Сер. матем., 52:6 (1988), 1272–1287; Math. USSR-Izv., 33:3 (1989), 597–612
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\paper О~классическом решении нелинейных эллиптических уравнений второго порядка
\jour Изв. АН СССР. Сер. матем.
\yr 1988
\vol 52
\issue 6
\pages 1272--1287
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\jour Math. USSR-Izv.
\yr 1989
\vol 33
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\pages 597--612
\crossref{https://doi.org/10.1070/IM1989v033n03ABEH000858}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/im1230
https://www.mathnet.ru/rus/im/v52/i6/p1272
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