Agarwal, Ravi P.; Prástaro, Agostino On the singular PDE’s geometry and boundary value problems. (English) Zbl 1180.35012 Appl. Anal. 88, No. 8, 1115-1131 (2009). Summary: A geometric formulation of singular partial differential equations (PDEs) is considered. Surgery techniques and integral bordism groups are utilized, following previous works by Prástaro on PDEs, in order to build global solutions crossing also singular points and to study their stability properties. Cited in 1 ReviewCited in 2 Documents MSC: 35A20 Analyticity in context of PDEs 55N22 Bordism and cobordism theories and formal group laws in algebraic topology 57R20 Characteristic classes and numbers in differential topology 58J32 Boundary value problems on manifolds 20H15 Other geometric groups, including crystallographic groups 35J75 Singular elliptic equations 35K67 Singular parabolic equations Keywords:surgery techniques; bordism groups in PDEs; geometric formulation PDFBibTeX XMLCite \textit{R. P. Agarwal} and \textit{A. Prástaro}, Appl. Anal. 88, No. 8, 1115--1131 (2009; Zbl 1180.35012) Full Text: DOI References: [1] Gromov M, Partial Differential Relations (1986) · doi:10.1007/978-3-662-02267-2 [2] DOI: 10.1016/0926-2245(94)00017-4 · Zbl 0808.58039 · doi:10.1016/0926-2245(94)00017-4 [3] Prástaro (ed.) A, Geometrodynamics Proceedings 1985 (1985) [4] Prástaro A, Boll. Un. Mat. Ital. 30 pp 977– (1991) [5] DOI: 10.1016/0034-4877(91)90063-S · Zbl 0771.58024 · doi:10.1016/0034-4877(91)90063-S [6] Prástaro A, Geometry of PDE’s and Mechanics (1996) · doi:10.1142/2986 [7] DOI: 10.1016/S0034-4877(97)84894-X · Zbl 0885.58094 · doi:10.1016/S0034-4877(97)84894-X [8] DOI: 10.1023/A:1005986024130 · Zbl 0924.58103 · doi:10.1023/A:1005986024130 [9] DOI: 10.1023/A:1006346916360 · Zbl 0949.35011 · doi:10.1023/A:1006346916360 [10] DOI: 10.1142/9789812562517 · doi:10.1142/9789812562517 [11] DOI: 10.1016/j.jmaa.2005.06.044 · Zbl 1100.35007 · doi:10.1016/j.jmaa.2005.06.044 [12] DOI: 10.1016/j.jmaa.2005.08.037 · Zbl 1160.58301 · doi:10.1016/j.jmaa.2005.08.037 [13] DOI: 10.1016/j.jmaa.2007.06.009 · Zbl 1135.35064 · doi:10.1016/j.jmaa.2007.06.009 [14] Prástaro A, Banach J. Math. Anal. 1 pp 139– (2007) · Zbl 1130.58014 · doi:10.15352/bjma/1240321564 [15] DOI: 10.1016/j.amc.2008.05.141 · Zbl 1161.35054 · doi:10.1016/j.amc.2008.05.141 [16] DOI: 10.1016/j.amc.2008.05.142 · Zbl 1161.35462 · doi:10.1016/j.amc.2008.05.142 [17] Goldschmidt H, J. Differential Geom. 1 pp 269– (1967) [18] Boardman JM, Publ. Math. I.H.E.S. 33 pp 21– (1967) · Zbl 0165.56803 · doi:10.1007/BF02684585 [19] Golubitsky M, Stable Mappings and Their Singularities (1973) · doi:10.1007/978-1-4615-7904-5 [20] Hirsh MW, Differential Topology (1976) · Zbl 0356.57001 · doi:10.1007/978-1-4684-9449-5 [21] Madsen IB, Annals of Mathematical Studies (1979) [22] Milnor J, Annals of Mathematical Studies 76 (1974) [23] Rudyak YB, On Thom Spectra, Orientability and Cobordism (1998) [24] Stong RE, Annals of Mathematics Studies (1968) [25] Switzer R, Algebraic Topology-Homotopy and Homology (1975) · doi:10.1007/978-3-642-61923-6 [26] DOI: 10.1007/BF02566923 · Zbl 0057.15502 · doi:10.1007/BF02566923 [27] Thom R, Bull. Soc. Math. France. 87 pp 455– (1954) [28] Thom R, Ann. Inst. Fourier 6 pp 43– (1955) · Zbl 0075.32104 · doi:10.5802/aif.60 [29] DOI: 10.2307/1970136 · Zbl 0097.38801 · doi:10.2307/1970136 [30] C.T.C Wall,Surgery on Compact Manifolds, London Math. Soc. Monographs 1, Academic Press, New York, 1970; 2nd edn (ed. A.A. Ranicki), Amer. Math. Soc. Surveys and Monographs 69, A.M.S., 1999 [31] Bryant RL, Exterior Differential Systems (1991) · doi:10.1007/978-1-4613-9714-4 [32] Cappel S, Surveys on Surgery Theory: Volume 1 (1999) [33] Goldschmidt, H and Spencer, D. 1977.Submanifolds and Over-determined Differential Operators, 319–356. Cambridge: Complex Analysis & Algebraic Geometry, Cambridge University Press. · Zbl 0364.58018 [34] Krasilśhchik IS, Geometry of Jet Spaces and Nonlinear Partial Differential Equations (1986) [35] DOI: 10.2307/2372381 · Zbl 0077.29701 · doi:10.2307/2372381 [36] Agarwal RP, Adv. Math. Sci. Appl. 17 pp 239– (2007) [37] Agarwal RP, Adv. Math. Sci. Appl. 17 pp 267– (2007) [38] Agarwal RP, J. Nonlinear Conv. Anal. 9 pp 417– (2008) [39] DOI: 10.1093/imamat/66.6.621 · Zbl 1073.34506 · doi:10.1093/imamat/66.6.621 [40] Agarwal RP, preprint (2008), Lecture delivered Department of Methods and Mathematical Models for Applied Sciences This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.