Nonlinear Muckenhoupt–Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations

A weighted norm inequality of Muckenhoupt–Wheeden type is obtained for gradients of solutions to a class of quasilinear equations with measure data on Reifenberg flat domains. This essentially leads to a resolution of an existence problem for quasilinear Riccati type equations with a gradient source...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 250; pp. 387 - 419
Main Author Phuc, Nguyen Cong
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.01.2014
Subjects
Capacity
Measure data
Muckenhoupt–Wheeden type inequalities
Quasilinear equations
Riccati type equations
Weighted norm inequalities
secondary
Riccati type equations
Weighted norm inequalities
Capacity
Measure data
Muckenhoupt–Wheeden type inequalities
Quasilinear equations
primary
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Summary:A weighted norm inequality of Muckenhoupt–Wheeden type is obtained for gradients of solutions to a class of quasilinear equations with measure data on Reifenberg flat domains. This essentially leads to a resolution of an existence problem for quasilinear Riccati type equations with a gradient source term of arbitrary power law growth.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2013.09.022