By Alberto Cialdea, Flavia Lanzara, Paolo Emilio Ricci
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Chervova and D. 4) where the bold tensor index α runs through the values 0, 1, 2, 3, 4, whereas its non-bold counterpart α runs through the values 0, 1, 2, 3. 4) stands for a column of four zeros. 1 The coordinate x4 parametrises a circle of radius 2m . 3) means that the extended coframe ϑ experiences a full turn in the (ϑ1 , ϑ2 )-plane as we move along this circle, coming back to the starting point. We extend our metric as 1 Aα gαβ − m12 Aα Aβ m . 5) means that we view electromagnetism as a perturbation (shear) of the extended metric.
Barles, A weak Bernstein method for fully nonlinear elliptic equations, Diﬀerential Integral Equations 4 (1991), 241–262.  G. Barles, F. Da Lio, On the generalized Dirichlet problem for viscous Hamilton– Jacobi equations, J. Math. Pures Appl. (9) 83 (2004), no. 1, 53–75.  L. G. Crandall, M. Kocan, A. Swiech, On viscosity solutions of fully nonlinear equations with measurable ingredients, Comm. Pure Appl. Math. 49 (1996), no. 4, 365–397.  I. Capuzzo Dolcetta, F. Leoni, A. Porretta, Viscous Hamilton-Jacobi equations.
Lions in . 1). Concerning the boundary behavior, if 1 < p ≤ 2 then u blows-up on ∂Ω, while if p > 2, then u is bounded and H¨ older continuous up to ∂Ω. This striking diﬀerence between the cases p ≤ 2 and p > 2 reﬂects a similar feature occurring in the study of the exit-time problem, see . Namely if 1 < p ≤ 2, the Dirichlet problem can be solved in the classical sense for any boundary datum g, while if p > 2 this is no longer true and there can be loss of boundary condition. In that case, the best one can expect, in general, is that the Dirichlet condition u = g is satisﬁed only in a generalized sense, see .
Analysis, partial differential equations and applications: The V.Maz'ya anniversary by Alberto Cialdea, Flavia Lanzara, Paolo Emilio Ricci