TY - JOUR
T1 - Nonlinear degenerate elliptic partial differential equations with critical growth conditions on the gradient
AU - Cho, Kwon
AU - Choe, Hi Jun
N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
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.
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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 -