Year: 2026
Type: article
Abstract: This paper is devoted to the study of weak Harnack inequalities for minimizers of nonlocal double phase functionals, whose prototype is given by $$ \iint _{\mathbb {R}^n\times \mathbb {R}^n} \left( \frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}+a(x,y)\frac{|u(x)-u(y)|^q}{|x-y|^{n+tq}}\right) \,dx\,dy, $$ ∬ R n × R n | u ( x ) - u ( y ) | p | x - y | n + s p + a ( x , y ) | u ( x ) - u ( y ) | q | x - y | n + t q d x d y , with $$a\ge 0$$ a ≥ 0 and $$0 0 < s , t < 1 < p ≤ q < ∞ . The core of our approach is based on expansion of positivity and several measure theoretic estimates stemming from a nonlocal Caccioppoli-type inequality. The main challenge lies in controlling the subtle interaction between the pointwise behaviour of the modulating coefficient $$a(\cdot ,\cdot )$$ a ( · , · ) and the structural exponents. In addition, we discuss a quantitative boundedness result for minimizers of such functionals.
Authors: Yuzhou Fang, Juha Kinnunen, Chao Zhang
Institutions: Harbin Institute of Technology, Aalto University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G1077737421, G3576484153, G6583590085
OpenAlex ID: W7129257792