The Reverse Hölder Inequality for the Solution to p-Harmonic Type System
نویسندگان
چکیده
Recently, amount of work about the A-harmonic equation for the differential forms has been done. In fact, the A-harmonic equation is an important generalization of the p-harmonic equation in R, p > 1, and the p-harmonic equation is a natural extension of the usual Laplace equation see 1 for the details . The reverse Hölder inequalities have been widely studied and frequently used in analysis and related fields, including partial differential equations and the theory of elasticity see 2 . In 1999, Nolder gave the reverse Hölder inequality for the solution to the A-harmonic equation in 3 , and different versions of Caccioppoli estimates have been established in 4–6 . In 2004, D’Onofrio and Iwaniec introduced the p-harmonic type system in 7 , which is an important extension of the conjugateA-harmonic equation. In 2007, Ding proved the following inequality in 8 .
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