Solvability of some integro-differential equations with the logarithmic Laplacian
Analysis of PDEs
2024-06-25 v1
Abstract
We address the existence in the sense of sequences of solutions for a certain integro-differential type problem involving the logarithmic Laplacian. The argument is based on the fixed point technique when such equation contains the operator without the Fredholm property. It is established that, under the reasonable technical conditions, the convergence in L^1(R^d) of the integral kernels yields the existence and convergence in L^2(R^d) of the solutions.
Keywords
Cite
@article{arxiv.2406.16126,
title = {Solvability of some integro-differential equations with the logarithmic Laplacian},
author = {Vitali Vougalter and Vitaly Volpert},
journal= {arXiv preprint arXiv:2406.16126},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2401.12458