Solvability of some integro-differential equations with the logarithmic Laplacian

Vitali Vougalter; Vitaly Volpert

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arXiv · 2406.16126

Solvability of some integro-differential equations with the logarithmic Laplacian

Vitali Vougalter·Vitaly Volpert

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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.

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Vitali Vougalter, Vitaly Volpert. 2024-06-23. Solvability of some integro-differential equations with the logarithmic Laplacian. https://arxiv.org/abs/2406.16126

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