2018/06/04 by Karthik Adimurthi, Adimurthi, Karthik, Sun‐Sig Byun +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1806.00944
openalex publication_date 2018/06/04 · openalex created_date 2022/08/25 · openalex updated_date 2026/07/28
In this paper, we study quasilinear parabolic equations with the nonlinearity\nstructure modeled after the p(x,t)-Laplacian on nonsmooth domains. The main\ngoal is to obtain end point Calder 'on-Zygmund type estimates in the variable\nexponent setting. In a recent work citebyun2016nonlinear, the estimates\nobtained were strictly above the natural exponent p(x,t) and hence there was\na gap between the natural energy estimates and the estimates above p(x,t)\n(see eqrefenergy and eqrefbyunok). Here, we bridge this gap to obtain the\nend point case of the estimates obtained in citebyun2016nonlinear. To this\nend, we make use of the parabolic Lipschitz truncation developed in citeKL\nand obtain significantly improved a priori estimates below the natural exponent\nwith stability of the constants. An important feature of the techniques used\nhere is that we make use of the unified intrinsic scaling introduced in\n citeadimurthi2018sharp, which enables us to handle both the singular and\ndegenerate cases simultaneously.\n