کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
841346 908507 2011 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Existence and regularity of nonnegative solution of a singular quasi-linear anisotropic elliptic boundary value problem with gradient terms
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Existence and regularity of nonnegative solution of a singular quasi-linear anisotropic elliptic boundary value problem with gradient terms
چکیده انگلیسی

In this paper, we consider the singular quasi-linear anisotropic elliptic boundary value problem equation(P){f1(u)uxx+uyy+g(u)|∇u|q+f(u)=0,(x,y)∈Ω,u|∂Ω=0, where ΩΩ is a smooth, bounded domain in R2R2; 00(t≠0), f1f1 is a smooth function in (−∞,+∞)(−∞,+∞) and is a non-decreasing function in (0,+∞)(0,+∞); g(t)≥0g(t)≥0, gg is a smooth function in (−∞,0)∪(0,+∞)(−∞,0)∪(0,+∞) and is a non-increasing function in (0,+∞)(0,+∞); f(t)>0f(t)>0, ff is a smooth function in (−∞,0)∪(0,+∞)(−∞,0)∪(0,+∞) and is a strictly decreasing function in (0,+∞)(0,+∞). Clearly, this is a boundary degenerate elliptic problem if f1(0)=0f1(0)=0. We show that the solution of the Dirichlet boundary value problem (P) is smooth in the interior and continuous or Lipschitz continuous up to the degenerate boundary and give the conditions for which gradients of solutions are bounded or unbounded. We believe that these results on regularity of the solution should be very useful.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 74, Issue 3, 1 February 2011, Pages 739–756
نویسندگان
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