A Note on Lebesgue Solvability of Elliptic Homogeneous Linear Equations with Measure Data

被引：2

作者：

Biliatto, Victor ^{[1
]}

Picon, Tiago ^{[2
]}

机构：

[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil

[2] Univ Sao Paulo, Dept Computacao & Matemat, BR-14040901 Ribeirao Preto, SP, Brazil

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Divergence-measure vector fields; Lebesgue solvability; L(1 )estimates; Elliptic equations; Canceling operators; SOBOLEV INEQUALITIES;

D O I：

10.1007/s12220-023-01457-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we present new results on solvability of the equation A*(D) f = mu for f is an element of L-p and positive measure data mu associated to an elliptic homogeneous linear differential operator A(D) of order m. Our method is based on (m, p)-energy control of mu giving a natural characterization for solutions when 1 <= p < infinity. We also obtain sufficient conditions in the limiting case p = infinity using new L-1 estimates on measures for elliptic and canceling operators.

引用

页数：18

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