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SOLUTIONS IN LEBESGUE SPACES TO NONLINEAR ELLIPTIC EQUATIONS WITH SUBNATURAL GROWTH TERMS

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Title: SOLUTIONS IN LEBESGUE SPACES TO NONLINEAR ELLIPTIC EQUATIONS WITH SUBNATURAL GROWTH TERMS
Authors: Seesanea, A. Browse this author
Verbitsky, I. E. Browse this author
Keywords: Quasilinear elliptic equation
measure data
p-Laplacian
fractional Laplacian
Wolff potential
Green function
Issue Date: Jun-2020
Publisher: American Mathematical Society
Journal Title: St Petersburg Mathematical Journal
Volume: 31
Issue: 3
Start Page: 557
End Page: 572
Publisher DOI: 10.1090/spmj/1614
Abstract: The paper is devoted to the existence problem for positive solutions u is an element of L-r(R-n), 0 < r < infinity, to the quasilinear elliptic equation -Delta(p)u = sigma u(q) in R-n in the subnatural growth case 0 < q < p - 1, where Delta(p)u = div(vertical bar del u vertical bar(P -2)del u) is the p-Laplacian with 1 < p < infinity, and sigma 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 Delta(p) such as the A-Laplacian divA(x, del u), or the fractional Laplacian (-Delta)(alpha) on R-n, as well as linear uniformly elliptic operators with bounded measurable coefficients div(A del u) on an arbitrary domain Omega subset of R-n with a positive Green function.
Rights: First published in St Petersburg Mathematical Journal 31(3), published by the American Mathematical Society. ©2020 American Mathematical Society.
https://creativecommons.org/licenses/by-nc-nd/2.0/
Type: article (author version)
URI: http://hdl.handle.net/2115/78730
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: Adisak Seesanea

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