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 in:Advances in mathematics (New York. 1965) 2014-01, Vol.250, p.387-419
Main Author: Phuc, Nguyen Cong
Format: Article
Language:English
Subjects:
Capacity
Measure data
Muckenhoupt–Wheeden type inequalities
Quasilinear equations
Riccati type equations
Weighted norm inequalities
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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