Abstract
In this paper, we first study the Riemann boundary value problem for Liapunov open curve in variable exponent space, we supplement the open curve as a closed one, and converted the problem to Riemann boundary value problem for closed curve in the variable exponent space, we solve the problem by discussing the singularity of the endpoints. Then we use these results to solve Hilbert boundary value problem for piecewise Liapunov closed curve in the variable exponent space, we also discuss the singularity of the discontinuity, we obtain the solvable conditions and explicit solutions of the Hilbert problem for piecewise Liapunov closed curve in the variable exponent space.
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This work was supported by National Natural Science Foundation of China (11601525, 12071485), Natural Science Foundation of Hunan Province (2020JJ4105).
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Wang, S., He, F. On the Variable Exponent Riemann Boundary Value Problem for Liapunov Open Curve. J Geom Anal 33, 62 (2023). https://doi.org/10.1007/s12220-022-01113-9
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DOI: https://doi.org/10.1007/s12220-022-01113-9