arXiv:2006.06276 Abstract | arXiv Analytics

arXiv:2006.06276 [math.AP]Abstract References Reviews Resources

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

Allami Benyaiche, Petteri Harjulehto, Peter Hästö, Arttu Karppinen

Published 2020-06-11Version 1

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.

Categories: math.AP

Subjects: 35J60, 35B65, 31C45

Keywords: weak harnack inequality, generalized orlicz growth, unbounded supersolutions, elliptic partial differential equations, study unbounded weak supersolutions

Related articles: Most relevant | Search more

arXiv:2304.04499 [math.AP] (Published 2023-04-10)

A note on the weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth

Mariia O. Savchenko, Igor I. Skrypnik, Yevgeniia A. Yevgenieva

arXiv:2203.13624 [math.AP] (Published 2022-03-25)

Stability of solutions to obstacle problems with generalized Orlicz growth

Petteri Harjulehto, Arttu Karppinen

arXiv:2006.08244 [math.AP] (Published 2020-06-15)

Hölder continuity of the minimizer of an obstacle problem with generalized Orlicz growth