Abstract
We consider a nonlinear degenerate elliptic partial differential equation with the critical growth condition on where g is sufficiently integrable and p is between 1 and ∞. Our first goal of this paper is to prove the existence of the solution.The main idea is to obtain the uniform L∞-estimate of suitable approximate solutions, employing a truncation technique and radially decreasing symmetrization techniques based on rearrangements. We also find an example of unbounded weak solution.
| Original language | English |
|---|---|
| Pages (from-to) | 3789-3796 |
| Number of pages | 8 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 123 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 1995 Dec |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
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Nonlinear degenerate elliptic partial differential equations with critical growth conditions on the gradient. / Cho, Kwon; Choe, Hi Jun.
In: Proceedings of the American Mathematical Society, Vol. 123, No. 12, 12.1995, p. 3789-3796.Research output: Contribution to journal › Article
TY - JOUR
T1 - Nonlinear degenerate elliptic partial differential equations with critical growth conditions on the gradient
AU - Cho, Kwon
AU - Choe, Hi Jun
PY - 1995/12
Y1 - 1995/12
N2 - We consider a nonlinear degenerate elliptic partial differential equation with the critical growth condition on where g is sufficiently integrable and p is between 1 and ∞. Our first goal of this paper is to prove the existence of the solution.The main idea is to obtain the uniform L∞-estimate of suitable approximate solutions, employing a truncation technique and radially decreasing symmetrization techniques based on rearrangements. We also find an example of unbounded weak solution.
AB - We consider a nonlinear degenerate elliptic partial differential equation with the critical growth condition on where g is sufficiently integrable and p is between 1 and ∞. Our first goal of this paper is to prove the existence of the solution.The main idea is to obtain the uniform L∞-estimate of suitable approximate solutions, employing a truncation technique and radially decreasing symmetrization techniques based on rearrangements. We also find an example of unbounded weak solution.
UR - http://www.scopus.com/inward/record.url?scp=21844490451&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=21844490451&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-1995-1285981-7
DO - 10.1090/S0002-9939-1995-1285981-7
M3 - Article
AN - SCOPUS:21844490451
VL - 123
SP - 3789
EP - 3796
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 12
ER -