A priori estimates and existence for quasi-linear elliptic equations

Zou, Heng
December 2008
Calculus of Variations & Partial Differential Equations;Dec2008, Vol. 33 Issue 4, p417
Academic Journal
We study the boundary value problem of quasi-linear elliptic equation where $${\Omega\subset\mathbb{R}^n}$$ ( n = 2) is a connected smooth domain, and the exponent $${m\in(1,n)}$$ is a positive number. Under appropriate conditions on the function B, a variety of results on a priori estimates, existence and non-existence of positive solutions have been established. The results are generically optimum for the canonical prototype B = | u| p-1 u, p > m - 1.


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