|
|
| |
| A Unified Boundary Behavior of Large Solutions to Hessian Equations |
| |
Citation： |
Zhijun ZHANG.A Unified Boundary Behavior of Large Solutions to Hessian Equations[J].Chinese Annals of Mathematics B,2020,41(4):601~614 |
| Page view： 487
Net amount： 471 |
Authors： |
Zhijun ZHANG; |
Foundation： |
This work was supported by the National Natural Science Foundation of China (No. 11571295) and RP of Shandong Higher Education Institutions (No. J17KA173). |
|
|
| Abstract： |
This paper is concerned with strictly k-convex large solutions to Hessian equations Sk(D2u(x)) = b(x)f(u(x)), x ∈ ?, where ? is a strictly (k k 1)-convex and bounded smooth domain in Rn, b ∈ C∞(?) is positive in ?, but may be vanishing on the boundary. Under a new structure condition on f at infinity, the author studies the refined boundary behavior of such solutions. The results are obtained in a more general setting than those in [Huang, Y., Boundary asymptotical behavior of large solutions to Hessian equations, Pacific J. Math., 244, 2010, 85–98], where f is regularly varying at infinity with index p > k. |
Keywords： |
Hessian equations, Strictly k-convex large solutions, Boundary behavior |
Classification： |
35J60, 35B40 |
|
|
Download PDF Full-Text
|
|
|
|
