An optimal gradient estimate for asymptotically regular variational integrals with multi-phase. (English) Zbl 1505.35065

Liang, Shuang; Zheng, Shenzhou

Rocky Mt. J. Math. 52, No. 6, 2071-2084 (2022).

Summary: We devote this article to the Calderón-Zygmund estimate for the minimizers of asymptotically regular variational integrals with multi-phase integrands. A local gradient \(L^q\)-estimate for such problem under a sharp regular assumption is obtained by approximating the solutions of asymptotically regular problems to the solutions of regular problems based on a new perturbation method, while the gradients of solutions close to infinity.

MSC:

35B45	A priori estimates in context of PDEs
35B65	Smoothness and regularity of solutions to PDEs
35J20	Variational methods for second-order elliptic equations

Keywords:

asymptotically regular; variational integrals with multi-phase; Calderón-Zygmund estimate

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