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Niveau: Supérieur, Licence, Bac+2

BOUNDED STABILITY FOR STRONGLY COUPLED CRITICAL ELLIPTIC SYSTEMS BELOW THE GEOMETRIC THRESHOLD OF THE CONFORMAL LAPLACIAN OLIVIER DRUET, EMMANUEL HEBEY, AND JEROME VETOIS To the memory of T. Aubin Abstract. We prove bounded stability for strongly coupled critical elliptic systems in the inhomogeneous context of a compact Riemannian manifold when the potential of the operator is less, in the sense of bilinear forms, than the geometric threshold potential of the conformal Laplacian. Let (M, g) be a smooth compact Riemannian manifold of dimension n ≥ 3. For p ≥ 1 an integer, let also Msp (R) denote the vector space of symmetrical p? p real matrices, and A be a C1 map from M to Msp (R). We write that A = (Aij)i,j , where the Aij 's are C1 real-valued functions in M . Let ∆g = ?divg? be the Laplace-Beltrami operator on M , and H1(M) be the Sobolev space of functions in L2(M) with one derivative in L2(M). The Hartree-Fock coupled systems of nonlinear Schrodinger equations we consider in this paper are written as ∆gui + p∑ j=1 Aij(x)uj = |U| 2??2 ui (0.1) in M for all i, where |U|2 = ∑p i=1 u 2 i , and 2 ? = 2nn?2 is the critical Sobolev expo- nent for the embeddings of the Sobolev space H1(M) into Lebesgue's spaces.

BOUNDED STABILITY FOR STRONGLY COUPLED CRITICAL ELLIPTIC SYSTEMS BELOW THE GEOMETRIC THRESHOLD OF THE CONFORMAL LAPLACIAN OLIVIER DRUET, EMMANUEL HEBEY, AND JEROME VETOIS To the memory of T. Aubin Abstract. We prove bounded stability for strongly coupled critical elliptic systems in the inhomogeneous context of a compact Riemannian manifold when the potential of the operator is less, in the sense of bilinear forms, than the geometric threshold potential of the conformal Laplacian. Let (M, g) be a smooth compact Riemannian manifold of dimension n ≥ 3. For p ≥ 1 an integer, let also Msp (R) denote the vector space of symmetrical p? p real matrices, and A be a C1 map from M to Msp (R). We write that A = (Aij)i,j , where the Aij 's are C1 real-valued functions in M . Let ∆g = ?divg? be the Laplace-Beltrami operator on M , and H1(M) be the Sobolev space of functions in L2(M) with one derivative in L2(M). The Hartree-Fock coupled systems of nonlinear Schrodinger equations we consider in this paper are written as ∆gui + p∑ j=1 Aij(x)uj = |U| 2??2 ui (0.1) in M for all i, where |U|2 = ∑p i=1 u 2 i , and 2 ? = 2nn?2 is the critical Sobolev expo- nent for the embeddings of the Sobolev space H1(M) into Lebesgue's spaces.

- valued schrodinger
- blow-up theory
- when ?a
- euclidean laplace-beltrami operator
- strong maximum
- up singulari- ties
- schrodinger equations
- limit system
- positive real

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Published by | profil-vieg-2012 |

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Language | English |

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