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Статья «SOLUTIONS IN LEBESGUE SPACES TO NONLINEAR ELLIPTIC EQUATIONS WITH SUBNATURAL GROWTH TERMS, "Алгебра и анализ"»

Авторы:
  • SEESANEA A.1
  • VERBITSKY I. E.2
стр. 216-238
Платно
1 Hokkaido University, 2 University of Missouri, Columbia
  • SDI: 007.001.0234-0852.2019.031.003.11
Ключевые слова:
  • quasilinear elliptic equation
  • measure data
  • p-Laplacian
  • fractional Laplacian
  • Wolff potential
  • Green function
Аннотация:
The paper is devoted to the existence problem for positive solutions u ? L(R), 0 < r < ?, to the quasilinear elliptic equation - ?u = ?U in R in the subnatural growth case 0 < q < p - 1, where ?u = div(|?u| ?u) is the p Laplacian with 1 < p < ?, and ? is a nonnegative measurable function (or measure) on R. The techniques rely on a study of general integral equations involving nonlinear potentials and related weighted norm inequalities. They are applicable to more general quasilinear elliptic operators in place of ? such as the A-Laplacian divA(x, ?u), or the Rational Laplacian (-?) on R, as well as linear uniformly elliptic operators with bounded measurable coefficients div(A?u) on an arbitrary domain ? C R with a positive Green function.

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