Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge–Bäcklund transformation, underlying symmetries among superficially different forms of the equations.
Mots clés : Hodge–Frobenius equations, Hodge–Bäcklund transformations, Nonlinear Hodge theory, A-harmonic forms
@article{AIHPC_2014__31_2_339_0, author = {Marini, Antonella and Otway, Thomas H.}, title = {Duality methods for a class of quasilinear systems}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {339--348}, publisher = {Elsevier}, volume = {31}, number = {2}, year = {2014}, doi = {10.1016/j.anihpc.2013.03.007}, mrnumber = {3181673}, zbl = {1300.35047}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.007/} }
TY - JOUR AU - Marini, Antonella AU - Otway, Thomas H. TI - Duality methods for a class of quasilinear systems JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 339 EP - 348 VL - 31 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.007/ DO - 10.1016/j.anihpc.2013.03.007 LA - en ID - AIHPC_2014__31_2_339_0 ER -
%0 Journal Article %A Marini, Antonella %A Otway, Thomas H. %T Duality methods for a class of quasilinear systems %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 339-348 %V 31 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.007/ %R 10.1016/j.anihpc.2013.03.007 %G en %F AIHPC_2014__31_2_339_0
Marini, Antonella; Otway, Thomas H. Duality methods for a class of quasilinear systems. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 2, pp. 339-348. doi : 10.1016/j.anihpc.2013.03.007. http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.007/
[1] Advances in differential forms and the A-harmonic equations, Math. Comput. Modelling 37 (2003), 1393-1426 | MR | Zbl
, ,[2] Calabi–Bernstein results for maximal surfaces in Lorentzian product spaces, J. Geom. Physics 59 (2009), 620-631 | MR | Zbl
, ,[3] A duality result between the minimal surface equation and the maximal surface equation, An. Acad. Brasil. Ciênc 73 (2001), 161-164 | MR | Zbl
, ,[4] Applied Exterior Calculus, Wiley, New York (1985) | MR | Zbl
,[5] Nonlinear Hodge theory on manifolds with boundary, Ann. Mat. Pura Appl. 177 (1999), 37-115 | MR | Zbl
, , ,[6] Extensions of the duality between minimal surfaces and maximal surfaces, Geom. Dedicata 151 (2011), 373-386 | MR | Zbl
,[7] On complex-valued solutions to a 2D eikonal equation. Part one: qualitative properties, Contemporary Math. 283 (1999), 203-229 | MR | Zbl
, ,[8] Approaching a partial differential equation of mixed elliptic–hyperbolic type, , , , (ed.), Ill-posed and Inverse Problems, VSP (2002), 263-276
, ,[9] Nonlinear Hodge–Frobenius equations and the Hodge–Bäcklund transformation, Proc. R. Soc. Edinburgh A 140 (2010), 787-819 | MR | Zbl
, ,[10] Constructing completely integrable fields by the method of generalized streamlines, arXiv:1205.7028 [math.AP] | Zbl
, ,[11] Decomposition and their application to nonlinear electro- and magnetostatic boundary value problems, , (ed.), Partial Differential Equations and Calculus of Variations, Lecture Notes in Mathematics vol. 1357, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo (1988) | Zbl
, ,[12] Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin (1966) | MR | Zbl
,[13] Nonlinear Hodge maps, J. Math. Phys. 41 (2000), 5745-5766 | MR | Zbl
,[14] Maps and fields with compressible density, Rend. Sem. Mat. Univ. Padova 111 (2004), 133-159 | EuDML | Numdam | MR | Zbl
,[15] The Dirichlet Problem for Elliptic–Hyperbolic Equations of Keldysh Type, Lecture Notes in Mathematics vol. 2043, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo (2012) | MR | Zbl
,[16] Hodge Decomposition: A Method for Solving Boundary Value Problems, Lecture Notes in Mathematics vol. 1607, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo (1995) | MR | Zbl
,[17] A nonlinear Hodge–de Rham theorem, Acta Math. 125 (1970), 57-73 | MR | Zbl
, ,[18] Nonlinear Hodge theory: Applications, Advances in Math. 31 (1979), 1-15 | MR | Zbl
, ,[19] Generalized Bernstein property and gravitational strings in Born–Infeld theory, Nonlinearity 20 (2007), 1193-1213 | MR | Zbl
, , ,[20] Classical solutions in the Born–Infeld theory, Proc. R. Soc. Lond. Ser. A 456 (2000), 615-640 | MR | Zbl
,Cité par Sources :