Sharp higher order Admas' inequality with exact growth condition on weighted Sobolev spaces

Abstract

This paper introduces a novel higher order Adams inequality that incorporates an exact growth condition for a class of weighted Sobolev spaces. Our rigorous proof confirms the validity of this inequality and provides insights into the optimal nature of the critical constant and the exponent within the denominator. Furthermore, we apply this inequality to study a class of ordinary differential equations (ODEs), where we successfully derive both a concept of the weak solution and a comprehensive regularity theory.

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Cited by in corpus (3)

• Trudinger-Moser type inequalities for the Hessian equation with logarithmic weights
• Sharp Sobolev and Adams-Trudinger-Moser inequalities for symmetric functions without boundary conditions on hyperbolic spaces
• On a supercritical Hardy-Sobolev type inequality with logarithmic term and related extremal problem