An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives

Abstract

We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend the previous result in [6] for unmixed $L_p$-estimates without weights.

29 Pages, submitted

References in corpus (4)

• An $L_q(L_p)$-theory for the time fractional evolution equations with variable coefficients
• $L_p$-estimates for time fractional parabolic equations with coefficients measurable in time
• $L_p$-estimates for time fractional parabolic equations in divergence form with measurable coefficients
• Weighted $L_q(L_p)$-estimate with Muckenhoupt weights for the diffusion-wave equations with time-fractional derivatives