We establish sufficient conditions for a uniform \(L^{p^\star }(\Omega )\) bound to imply a uniform \(L^\infty (\Omega )\) bound for positive weak solutions of subcritical p-Laplacian equations. We also provide an equivalent result for sequences of boundary-value problems. As consequences, we prove that any set of solutions with finite energy is \(L^\infty (\Omega )\) a priori bounded, and also obtain an alternative proof of the existence of a priori bounds for subcritical power like nonlinearities.

中文翻译：

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亚临界p -Laplacian方程的一致$$ L ^ {p ^ *} $$ L p ∗ A先验界与一致$$ L ^ {\ infty} $$ L∞A先验界之间的等价关系

我们建立了一个统一的\（L ^ {p ^ \ star}（\ Omega）\）的充分条件，以暗示一个次临界p -Laplacian的正弱解的统一\（L ^ \ infty（\ Omega）\）方程。我们还为边值问题序列提供了等效的结果。作为后果，我们证明了任何一组具有有限能源解决方案是\（L ^ \ infty（\欧米茄）\）先验界，并且还获得的存在的另一种证明先验界限为亚临界功率等的非线性。