AN INTERPOLATION APPROACH TO L∞ A PRIORI ESTIMATES FOR ELLIPTIC PROBLEMS WITH NONLINEARITY ON THE BOUNDARY

被引：0

作者：

Chhetri, Maya ^{[1
]}

Mavinga, Nsoki ^{[2
]}

Pardo, Rosa ^{[3
]}

机构：

[1] Univ North Carolina Greensboro, Dept Math & Stat, Greensboro, NC 27402 USA

[2] Swarthmore Coll, Dept Math & Stat, Swarthmore, PA 19081 USA

[3] Univ Complutense Madrid, Dept Math Anal & Appl Math, Madrid 28040, Spain

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2025年 / 153卷 / 04期

基金：

美国国家科学基金会;

关键词：

Elliptic problem; nonlinear boundary conditions; subcritical; Gagliardo-Nirenberg interpolation inequality; L-infinity a priori estimate; EQUATIONS; BIFURCATION;

D O I：

10.1090/proc/17075

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. We establish an explicit L infinity(Omega) a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their H1(Omega) norms. To prove our result, we combine in a novel way Moser type estimates together with elliptic regularity and Gagliardo-Nirenberg interpolation inequality. We illustrate our result with an application to subcritical problems satisfying Ambrosetti-Rabinowitz condition.

引用

页码：1585 / 1593

页数：9

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