Calderón–Zygmund estimates in generalized Orlicz spaces

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Abstract

We establish the W2,φ()-solvability of the linear elliptic equations in non-divergence form under a suitable, essentially minimal, condition of the generalized Orlicz function φ()=φ(x,t), by deriving Calderón–Zygmund type estimates. The class of generalized Orlicz spaces we consider here contains as special cases classical Lebesgue and Orlicz spaces, as well as non-standard growth cases like variable exponent and double phase growth.

MSC

35J25
46E30
35A01

Keywords

Second order equations
Generalized Orlicz spaces
Calderón–Zygmund estimates

Cited by (0)

This work was supported by the Finnish Academy of Science and Letters, Väisälä Foundation. J. Ok was supported by the National Research Foundation of Korea funded by Korean Government (NRF-2017R1C1B2010328).