Mixed type boundary value problems for Laplace–Beltrami equation on a surface with the Lipschitz boundary

References

[1] T. Buchukuri, R. Duduchava, D. Kapanadze and M. Tsaava, Localization of a Helmholtz boundary value problem in a domain with piecewise-smooth boundary, Proc. A. Razmadze Math. Inst. 162 (2013), 37–44. Search in Google Scholar

[2] L. P. Castro, R. Duduchava and F.-O. Speck, Localization and minimal normalization of some basic mixed boundary value problems, Factorization, Singular Operators and Related Problems (Funchal 2002), Kluwer Academic, Dordrecht (2003), 73–100. 10.1007/978-94-017-0227-0_7Search in Google Scholar

[3] L. P. Castro, R. Duduchava and F.-O. Speck, Mixed impedance boundary value problems for the Laplace–Beltrami equation, to appear in J. Integral Equations Appl., https://projecteuclid.org/euclid.jiea/1580958082. 10.1216/jie.2020.32.275Search in Google Scholar

[4] L. P. Castro and D. Kapanadze, Wave diffraction by wedges having arbitrary aperture angle, J. Math. Anal. Appl. 421 (2015), no. 2, 1295–1314. 10.1016/j.jmaa.2014.07.080Search in Google Scholar

[5] M. Costabel and E. Stephan, Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation, Mathematical Models and Methods in Mechanics, Banach Center Publ. 15, PWN, Warsaw (1985), 175–251. 10.4064/-15-1-175-251Search in Google Scholar

[6] M. Dauge, Elliptic Boundary Value Problems on Corner Domains. Smoothness and Asymptotics of Solutions, Lecture Notes in Math. 1341, Springer, Berlin, 1988. 10.1007/BFb0086682Search in Google Scholar

[7] V. D. Didenko and R. Duduchava, Mellin convolution operators in Bessel potential spaces, J. Math. Anal. Appl. 443 (2016), no. 2, 707–731. 10.1016/j.jmaa.2016.05.043Search in Google Scholar

[8] R. Duduchava, Integral Equations with Fixed Singularities, BSB B. G. Teubner, Leipzig, 1979. Search in Google Scholar

[9] R. Duduchava, The Green formula and layer potentials, Integral Equations Operator Theory 41 (2001), no. 2, 127–178. 10.1007/BF01295303Search in Google Scholar

[10] R. Duduchava, Partial differential equations on hypersurfaces, Mem. Differ. Equ. Math. Phys. 48 (2009), 19–74. Search in Google Scholar

[11] R. Duduchava, Mellin convolution operators in Bessel potential spaces with admissible meromorphic kernels, Mem. Differ. Equ. Math. Phys. 60 (2013), 135–177. Search in Google Scholar

[12] R. Duduchava, D. Natroshvili and E. Shargorodsky, Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts. I, Georgian Math. J. 2 (1995), no. 2, 123–140. 10.1515/GMJ.1995.123Search in Google Scholar

[13] R. Duduchava and M. Tsaava, Mixed boundary value problems for the Laplace–Beltrami equation, Complex Var. Elliptic Equ. 63 (2018), no. 10, 1468–1496. 10.1080/17476933.2017.1385066Search in Google Scholar

[14] R. Duduchava and M. Tsaava, Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain, Georgian Math. J. 27 (2020), no. 2, 211–231. 10.1515/gmj-2019-2031Search in Google Scholar

[15] R. Duduchava, M. Tsaava and T. Tsutsunava, Mixed boundary value problem on hypersurfaces, Int. J. Differ. Equ. 2014 (2014), Article ID 245350. 10.1155/2014/245350Search in Google Scholar

[16] R. Dudučava, Wiener–Hopf integral operators with discontinuous symbols (in Russian), Dokl. Akad. Nauk SSSR 211 (1973), 277–280; translation in Sov. Math. Doklady 14 (1973), 1001–1005. Search in Google Scholar

[17] P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monogr. Stud. Math. 24, Pitman, Boston, 1985. Search in Google Scholar

[18] P. Grisvard, Singularities in Boundary Value Problems, Rech. Math. Appl. 22, Masson, Paris, 1992. Search in Google Scholar

[19] G. C. Hsiao and W. L. Wendland, Boundary Integral Equations, Appl. Math. Sci. 164, Springer, Berlin, 2008. 10.1007/978-3-540-68545-6Search in Google Scholar

[20] V. A. Kondrat’ev, Boundary value problems for elliptic equations in domains with conical or angular points (in Russian), Trudy Moskov. Mat. Obšč. 16 (1967), 209–292; translation in Trans. Moscow Math. Soc. 16 (1967), 227–313. Search in Google Scholar

[21] P. A. Krutitskii, The Helmholtz equation in the exterior of slits in a plane with different impedance boundary conditions on opposite sides of the slits, Quart. Appl. Math. 67 (2009), no. 1, 73–92. 10.1090/S0033-569X-08-01117-4Search in Google Scholar

[22] A. Lorenzi, A mixed boundary value problem for the Laplace equation in an angle (1st part), Rend. Semin. Mat. Univ. Padova 54 (1975), 147–183. Search in Google Scholar

[23] A. Lorenzi, A mixed boundary value problem for the Laplace equation in an angle (2nd part), Rend. Semin. Mat. Univ. Padova 55 (1976), 7–43. Search in Google Scholar

[24] M. Merigot, Régularité des dérivées de la solution du problème de Dirichlet dans un secteur plan, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A356–A359. Search in Google Scholar

[25] M. Merigot, Régularité des dérivées de la solution du problème de Dirichlet dans un secteur plan, Matematiche (Catania) 27 (1972), 324–359. Search in Google Scholar

[26] M. Merigot, Etude du problème Δ⁢u=f dans un polygone plan. Inégalités à priori, Boll. Unione Mat. Ital. (4) 10 (1974), 577–597. Search in Google Scholar

[27] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, 2nd ed., Johann Ambrosius Barth, Heidelberg, 1995. Search in Google Scholar