Keywords and phrases: hyperbolic equations, removable sets, Hausdorff measure.
Received: October 15, 2024; Accepted: December 7, 2024; Published: December 19, 2024
How to cite this article: I. Ly, M. Ouedraogo, B. Bella and T. Ouedraogo, Removable sets for the wave equations in terms of Hausdorff measure, International Journal of Numerical Methods and Applications 25(1) (2025), 87-101. https://doi.org/10.17654/0975045225004
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References: [1] S. Bochner, Weak solutions of linear partial differential equations, J. Math. Pures Appl. (9) 35 (1956), 193-202. [2] D. Fedchenko and N. Tarkhanov, A Radó theorem for the porous medium equation, Bol. Soc. Mat. Mex. III 24(2) (2018), 427-437. [3] H. Federer, Geometric Measure Theory, Springer-Verlag, Berlin, 1969. [4] R. Harvey and J. C. Polking, Removable singularities of solutions of linear partial differential equations, Acta Math. 125(1-2) (1970), 39-56. [5] R. Harvey and J. C. Polking, A notion of capacity which characterizes removable singularities, Trans. Amer. Math. Soc. 169 (1972), 183-195. [6] C. Gonzales-Flores and E. S. Zeron, Radó’s theorem for factorisations of the Laplace operator, Bol. Soc. Mat. Mexicana 18(2) (2012), 143-149. [7] T. Kilpeläinen, A. Radó type theorem for p-harmonic functions in the plane, Electron. J. Differential Equations 9 (1994), 1-4. [8] T. Kilpeläinen, P. Koskela and O. Martio, On the fusion problem for degenerate elliptic equations, Comm. Partial Differential Equations 20(3-4) (1995), 485-497. [9] J. Král, Some extension results concerning harmonic functions, J. London Math. Soc. 28 (1983), 62-70. [10] I. Ly and N. Tarkhanov, A Radó theorem for p-harmonic functions, Bol. Soc. Mat. Mex. III 22(2) (2016), 461-472. [11] O. Martio, Counterexamples for unique continuation, Manuscripta Math. 60 (1988), 21-47. [12] T. Radó, Subharmonic Functions, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 5, Heft 1, Springer, Berlin, 1937. [13] Yu. G. Reshetnyak, Space mappings with bounded distortion, Transl. of Math. Monographs, Vol. 73, Amer. Math. Soc., Providence, R.I., 1989. [14] J. Serrin, Local behaviour of solutions of quasilinear equations, Acta Math. 111 (1964), 247-302. [15] N. Tarkhanov, The Analysis of Solutions of Elliptic Equations, Kluwer Academic Publishers, Dordrecht, NL, 1995. [16] L. Verón, Singularities of solutions of second order quasilinear equations, Pitman Research Notes in Mathematics Series, 353, Longman, Harlow, 1996.
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