Abstract
We establish existence results for a class of mixed anisotropic and nonlocal p-Laplace equations with singular nonlinearities. We consider both constant and variable singular exponents. Our argument is based on an approximation method. To this end, we also discuss the necessary regularity properties of weak solutions of the associated non-singular problems. More precisely, we obtain local boundedness of subsolutions, the Harnack inequality for solutions and the weak Harnack inequality for supersolutions.
Original language | English |
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Pages (from-to) | 697-715 |
Number of pages | 19 |
Journal | Forum Mathematicum |
Volume | 36 |
Issue number | 3 |
DOIs | |
State | Published - 1 May 2024 |
Externally published | Yes |
Keywords
- Mixed anisotropic and nonlocal p-Laplace equation
- existence
- regularity
- singular problem
- variable exponent
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics