<p>We obtain new <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_2929_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$L_p$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> estimates for subsolutions to fully nonlinear equations. Based on our <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_2929_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$L_p$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> estimates, we further study several topics such as the third and fourth order derivative estimates for concave fully nonlinear equations, critical exponents of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_2929_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$L_p$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> estimates and maximum principles, and the existence and uniqueness of solutions to fully nonlinear equations on the torus with free terms in the <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_2929_Article_IEq7.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$L_p$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> spaces or in the space of Radon measures.</p>

Second order $L_p$ estimates for subsolutions of fully nonlinear equations

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2025年2月6日

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Hongjie Dong,
Shuhei Kitano

摘要

We obtain new $L_p$ $L_{p}$ estimates for subsolutions to fully nonlinear equations. Based on our $L_p$ $L_{p}$ estimates, we further study several topics such as the third and fourth order derivative estimates for concave fully nonlinear equations, critical exponents of $L_p$ $L_{p}$ estimates and maximum principles, and the existence and uniqueness of solutions to fully nonlinear equations on the torus with free terms in the $L_p$ $L_{p}$ spaces or in the space of Radon measures.

Second order \(L_p\) estimates for subsolutions of fully nonlinear equations

摘要