We consider boundary blowup problems for k-curvature equations of the form \(H_k[u] = f(u)g(|Du|)\) in a bounded smooth domain \(\Omega \subset \mathbb {R}^n\), where f(s) behaves like \(s^p\) as \(s \rightarrow \infty \) and g(t) behaves like \(t^{-q}\) as \(t \rightarrow \infty \). We obtain the exact principal blowup rate of a solution u near the boundary \(\partial \Omega \) under some conditions.

中文翻译：

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k曲率方程的边界爆破解的边界附近的精确主爆率

我们考虑有界光滑域\（\ Omega \ subset \ mathbb {R} ^ n中形式为\（H_k [u] = f（u）g（| Du |）\）的k个曲率方程的边界爆破问题\） ，其中˚F（小号）表现得如同\（S ^ p \）作为\（S \ RIGHTARROW \ infty \）和克（吨）等的行为\（T ^ { - q} \）作为\（T \ RIGHTARROW \ infty \）。在某些条件下，我们获得了边界\（\ partial \ Omega \）附近溶液u的精确主爆率。