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Bubbling along boundary geodesics near the second critical exponent

Manuel del Pino, Monica Musso, Frank Pacard (2010)

Journal of the European Mathematical Society

The role of the second critical exponent p = ( n + 1 ) / ( n - 3 ) , the Sobolev critical exponent in one dimension less, is investigated for the classical Lane–Emden–Fowler problem Δ u + u p = 0 , u > 0 under zero Dirichlet boundary conditions, in a domain Ω in ℝ n with bounded, smooth boundary. Given Γ , a geodesic of the boundary with negative inner normal curvature we find that for p = ( n + 1 ) / ( n - 3 - ε ) , there exists a solution u ε such that | ∇ u ε | 2 converges weakly to a Dirac measure on Γ as ε → 0 + , provided that Γ is nondegenerate in the sense of second variations of...

Bundle functors with the point property which admit prolongation of connections

W. M. Mikulski (2010)

Annales Polonici Mathematici

Let F:ℳ f →ℱℳ be a bundle functor with the point property F(pt) = pt, where pt is a one-point manifold. We prove that F is product preserving if and only if for any m and n there is an ℱ ℳ m , n -canonical construction D of general connections D(Γ) on Fp:FY → FM from general connections Γ on fibred manifolds p:Y → M.

BV solutions and viscosity approximations of rate-independent systems

Alexander Mielke, Riccarda Rossi, Giuseppe Savaré (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In the nonconvex case, solutions of rate-independent systems may develop jumps as a function of time. To model such jumps, we adopt the philosophy that rate-independence should be considered as limit of systems with smaller and smaller viscosity. For the finite-dimensional case we study the vanishing-viscosity limit of doubly nonlinear equations given in terms of a differentiable energy functional and a dissipation potential that is a viscous regularization of a given rate-independent dissipation...

BV solutions and viscosity approximations of rate-independent systems∗

Alexander Mielke, Riccarda Rossi, Giuseppe Savaré (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In the nonconvex case, solutions of rate-independent systems may develop jumps as a function of time. To model such jumps, we adopt the philosophy that rate-independence should be considered as limit of systems with smaller and smaller viscosity. For the finite-dimensional case we study the vanishing-viscosity limit of doubly nonlinear equations given in terms of a differentiable energy functional and a dissipation potential that is a viscous regularization...

Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. II

Takashi Aoki (1986)

Annales de l'institut Fourier

Soit P un opérateur pseudodifférentiel (ou microdifférentiel) tel que exp P soit aussi un opérateur pseudodifférentiel. Alors le symbole de exp P s’ecrit exp q avec un symbole q . Pour la réciproque, si Q est un opérateur à symbole exp q , il existe un opérateur P tel que Q = exp P . Tous ces résultats reposent sur la théorie développée dans la Note I de cette série. Comme application, on obtient une condition suffisante d’inversibilité pour les opérateurs pseudodifférentiels d’ordre infini.

Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. I

Takashi Aoki (1983)

Annales de l'institut Fourier

Cet article s’intéresse au calcul symbolique des opérateurs microdifférentiels avec symboles exponentiels. On donne la loi de composition des symboles exponentiels. Comme application, on trouve une condition suffisante d’ellipticité pour les opérateurs microdifférentiels d’ordre infini.

Calcul Jacobien

Bernard Morin (1975)

Annales scientifiques de l'École Normale Supérieure

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