The regularity of weak solutions for a class of A-harmonic equations

Abstract

Abstract: To study the gradient estimations of solutions for a class of elliptic harmonic equations in Besov space, appropriate structural conditions for operator A and operator B were established first. Then, a vector field function was introduced, in conjunction with the structural conditions of operator A, to derive a quasi-monotonicity inequality. The growth of the gradient was estimated by employing finite difference methods, Hölder’s inequality, and Young’s inequality. Finally, the regularity results for the gradient of the solutions in the Besov space were obtainedby utilizing embedding theorems.

Key words: A-harmonic equation, Hölder inequality, Young inequality, regularity

CLC Number:

O152.5

LIU Wen-ru, LU Yue-ming. The regularity of weak solutions for a class of A-harmonic equations[J]. Journal of Lanzhou University of Technology, 2026, 52(1): 158-163.

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