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Article Contents

# Regularity of solutions to an integral equation associated with Bessel potential

• In this paper, we study the regularity of the positive solutions to an integral equation associated with the Bessel potential. The kernel estimates for the Bessel potential plays an essential role in deriving such regularity results. First, we apply the regularity lifting by contracting operators to get the $L^\infty$ estimate. Then, we use the regularity lifting by combinations of contracting and shrinking operators, which was recently developed in [4] and [5], to prove the Lipschitz continuity estimate. Our regularity results here have been recently extended to positive solutions to an integral system associated with Bessel potential [9].
Mathematics Subject Classification: Primary: 45E10; Secondary: 35J60.

 Citation:

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