Calderón–Zygmund estimates for parabolic p(x,t)-Laplacian systems

• Autores: Paolo Baroni , Verena Bögelein
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 30, Nº 4, 2014, págs. 1355-1386
• Idioma: inglés
• DOI: 10.4171/RMI/817
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• Resumen

  • We prove local Calderón–Zygmund estimates for weak solutions of the evolutionary p(x,t)-Laplacian system ∂tu−div (a(x,t)|Du|p(x,t)−2Du)=div (|F|p(x,t)−2F) under the classical hypothesis of logarithmic continuity for the variable exponent p(x,t). More precisely, we show that the spatial gradient Du of the solution is as integrable as the right-hand side F, i.e., |F|p(⋅)∈Lqloc ⟹ |Du|p(⋅)∈Lqlocfor any q>1, together with quantitative estimates. Thereby we allow the presence of eventually discontinuous coefficients a(x,t), requiring only a VMO condition with respect to the spatial variable x.