An elliptic problem of the Prandtl-Batchelor type with a singularity
Analysis of PDEs
2023-06-23 v1 Functional Analysis
Abstract
We establish the existence of at least two solutions of the {\it Prandtl-Batchelor} like elliptic problem driven by a power nonlinearity and a singular term. The associated energy functional is nondifferentiable and hence the usual variational techniques do not work. We shall use a novel approach in tackling the associated energy functional by a sequence of functionals and a {\it cutoff function}. Our main tools are fundamental elliptic regularity theory and the mountain pass theorem.
Keywords
Cite
@article{arxiv.2306.12744,
title = {An elliptic problem of the Prandtl-Batchelor type with a singularity},
author = {Debajyoti Choudhuri and Dušan D. Repovš},
journal= {arXiv preprint arXiv:2306.12744},
year = {2023}
}