|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
SOLUTIONS IN LEBESGUE SPACES TO NONLINEAR ELLIPTIC EQUATIONS WITH SUBNATURAL GROWTH TERMS
This item is licensed under:Creative Commons Attribution-NonCommercial-NoDerivs 2.0 Generic
| 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
|
