Kavli Affiliate: Hsiao-Mei (Sherry) Cho
| First 5 Authors: [#item_custom_name[1, [#item_custom_name[2, [#item_custom_name[3, [#item_custom_name[4, [#item_custom_name[5| Summary:We establish an optimal Calderón-Zygmund theory for nonuniformly elliptic double phase problems with matrix weights. For $1<p<q<infty$, $a(cdot)in C^0,α(Ω)$ ($0<αle1$), and a symmetric, almost everywhere positive definite matrix weight $M$ with $|M(x)|,|M(x)^-1|leΛ$ for some constant $Λge 1$ and small $|log M|_mathrmBMO$, we prove, for every $γ>1$, $$ (|M F|^p+a(x)|M F|^q)in L^γ_mathrmloc ;Longrightarrow; (|M Du|^p+a(x)|M Du|^q)in L^γ_mathrmloc. $$ Our argument combines a freezing of the logarithm of the matrix field, $log M$, with a fractional maximal-operator method governed by the Muckenhoupt-Wheeden $mathcalA_p,s$ classes (where $1/s=1/p-α/(nq)$). This yields scale-invariant comparison and level-set estimates and precludes Lavrentiev gaps at the sharp threshold $q/ple 1+α/n$. Our result recovers the identity case $,Mequiv rm I_n,$, i.e., the classical (unweighted) Calderón-Zygmund theory for double-phase problems.| Search Query: arXiv Query: search_query=au:Cho OR all:Hsiao-Mei&id_list=&start=0&max_results=3Read More