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

共 50 条

[41] ON LP ESTIMATES FOR QUASI-ELLIPTIC BOUNDARY PROBLEMS
ARKERYD, L
MATHEMATICA SCANDINAVICA, 1969, 24 (01) : 141 - &
[42] On estimates for solutions of elliptic boundary value problems in a layer
V. A. Nikishkin
Differential Equations, 2011, 47 : 446 - 450
[43] ESTIMATES AND EXISTENCE THEOREMS FOR ELLIPTIC BOUNDARY VALUE PROBLEMS
BROWDER, FE
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1959, 45 (03) : 365 - 372
[44] On Estimates for Solutions of Elliptic Boundary Value Problems in a Layer
Nikishkin, V. A.
DIFFERENTIAL EQUATIONS, 2011, 47 (03) : 446 - 450
[45] Nonlinearity identification in divergence type elliptic boundary value problems
Voisei, M. D.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 335 (02) : 948 - 961
[46] Optimal a priori estimates for higher order finite elements for elliptic interface problems
Li, Jingzhi
Melenk, Jens Markus
Wohlmuth, Barbara
Zou, Jun
APPLIED NUMERICAL MATHEMATICS, 2010, 60 (1-2) : 19 - 37
[47] A priori error estimates for elliptic optimal control problems with a bilinear state equation
Kroener, Axel
Vexler, Boris
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 230 (02) : 781 - 802
[48] Remarks on computable a priori error estimates for finite element solutions of elliptic problems
Takayasu, Akitoshi
Liu, Xuefeng
Oishi, Shin'ichi
IEICE NONLINEAR THEORY AND ITS APPLICATIONS, 2014, 5 (01): : 53 - 63
[49] ANOTHER APPROACH TO ELLIPTIC BOUNDARY PROBLEMS
PEETRE, J
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1961, 14 (04) : 711 - &
[50] A priori error estimates of multiblock mortar expanded mixed method for elliptic problems
Arshad, Muhammad
APPLIED NUMERICAL MATHEMATICS, 2020, 157 : 670 - 686

← 1 2 3 4 5 →