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Quasilinear Equations with Exponential Reactions and Measure Data on Carnot Groups
Abstract
In this paper, we establish existence and pointwise Wolff potential bounds for nonnegative solutions of −Δ𝔾,pu=Hl(αuβ)+μ on Carnot groups, where Hl(t)=et−∑j=0l−1tj/j! and μ is a nonnegative Radon measure. Under suitable conditions on the reaction parameters, we treat arbitrary open sets in the subcritical range 1<p<Q under a maximal potential condition, and bounded domains in the critical case p=Q under a small total mass condition.
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BibTeX
@misc{ma2026quasilinear,
title = {{Quasilinear Equations with Exponential Reactions and Measure Data on Carnot Groups}},
author = {Shiguang Ma and Zijian Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.19704},
eprint = {2609.19704},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19704},
}
RIS
TY - UNPB
TI - Quasilinear Equations with Exponential Reactions and Measure Data on Carnot Groups
AU - Shiguang Ma
AU - Zijian Wang
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.19704
UR - https://arxiv.org/abs/2609.19704
AB - In this paper, we establish existence and pointwise Wolff potential bounds for nonnegative solutions of −Δ_𝔾,pu=H_l(αu^β)+μ on Carnot groups, where H_l(t)=e^t−∑_j=0^l−1t^j/j! and μ is a nonnegative Radon measure. Under suitable conditions on the reaction parameters, we treat arbitrary open sets in the subcritical range 1<p<Q under a maximal potential condition, and bounded domains in the critical case p=Q under a small total mass condition.
ER -