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arXiv · 2006.06276

The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth

Allami Benyaiche·Petteri Harjulehto·Peter Hästö·Arttu Karppinen
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Abstract

We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak--Orlicz) growth. We show that they satisfy the weak Harnack inequality with optimal exponent provided that they belong to a suitable Lebesgue or Sobolev space. Furthermore, we establish the sharpness of our central assumptions.

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Allami Benyaiche, Petteri Harjulehto, Peter Hästö, Arttu Karppinen. 2020-06-11. The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth. https://doi.org/10.1016/j.jde.2020.11.007

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