The Experts below are selected from a list of 11361 Experts worldwide ranked by ideXlab platform
Hendrik Vogt - One of the best experts on this subject based on the ideXlab platform.
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L_∞-Estimates for the Torsion Function and L_∞-Growth of Semigroups Satisfying Gaussian Bounds
Potential Analysis, 2019Co-Authors: Hendrik VogtAbstract:We investigate selfadjoint C _0-semigroups on Euclidean Domains satisfying Gaussian upper bounds. Major examples are semigroups generated by second order uniformly elliptic operators with Kato potentials and magnetic fields. We study the long time behaviour of the L _ ∞ operator norm of the semigroup. As an application we prove a new L _ ∞ -bound for the torsion function of a Euclidean Domain that is close to optimal.
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l estimates for the torsion function and l growth of semigroups satisfying gaussian bounds
Potential Analysis, 2019Co-Authors: Hendrik VogtAbstract:We investigate selfadjoint C0-semigroups on Euclidean Domains satisfying Gaussian upper bounds. Major examples are semigroups generated by second order uniformly elliptic operators with Kato potentials and magnetic fields. We study the long time behaviour of the L∞ operator norm of the semigroup. As an application we prove a new L∞-bound for the torsion function of a Euclidean Domain that is close to optimal.
Pierre J Clavier - One of the best experts on this subject based on the ideXlab platform.
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Alien calculus and a Schwinger–Dyson equation: two-point function with a nonperturbative mass scale
Letters in Mathematical Physics, 2018Co-Authors: Marc P. Bellon, Pierre J ClavierAbstract:Starting from the Schwinger–Dyson equation and the renormalization group equation for the massless Wess–Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep Euclidean Domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive $$\beta $$ β -function. On the other side, we have a singularity of the propagator for timelike momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.
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Alien calculus and a Schwinger–Dyson equation: two-point function with a nonperturbative mass scale
Letters in Mathematical Physics, 2018Co-Authors: Marc Bellon, Pierre J ClavierAbstract:Starting from the Schwinger–Dyson equation and the renormalization group equation for the massless Wess–Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep Euclidean Domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive β-function. On the other side, we have a singularity of the propagator for timelike momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.
Marc Bellon - One of the best experts on this subject based on the ideXlab platform.
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Alien calculus and a Schwinger–Dyson equation: two-point function with a nonperturbative mass scale
Letters in Mathematical Physics, 2018Co-Authors: Marc Bellon, Pierre J ClavierAbstract:Starting from the Schwinger–Dyson equation and the renormalization group equation for the massless Wess–Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep Euclidean Domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive β-function. On the other side, we have a singularity of the propagator for timelike momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.
Marc P. Bellon - One of the best experts on this subject based on the ideXlab platform.
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Alien calculus and a Schwinger–Dyson equation: two-point function with a nonperturbative mass scale
Letters in Mathematical Physics, 2018Co-Authors: Marc P. Bellon, Pierre J ClavierAbstract:Starting from the Schwinger–Dyson equation and the renormalization group equation for the massless Wess–Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep Euclidean Domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive $$\beta $$ β -function. On the other side, we have a singularity of the propagator for timelike momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.
Luc Nguyen - One of the best experts on this subject based on the ideXlab platform.
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Existence and Uniqueness to a Fully Nonlinear Version of the Loewner–Nirenberg Problem
Communications in Mathematics and Statistics, 2018Co-Authors: María Del Mar González, Luc NguyenAbstract:We consider the problem of finding on a given Euclidean Domain $$\Omega $$ Ω of dimension $$n \ge 3$$ n ≥ 3 a complete conformally flat metric whose Schouten curvature A satisfies some equations of the form $$f(\lambda (-A)) = 1$$ f ( λ ( - A ) ) = 1 . This generalizes a problem considered by Loewner and Nirenberg for the scalar curvature. We prove the existence and uniqueness of such metric when the boundary $$\partial \Omega $$ ∂ Ω is a smooth bounded hypersurface (of codimension one). When $$\partial \Omega $$ ∂ Ω contains a compact smooth submanifold $$\Sigma $$ Σ of higher codimension with $$\partial \Omega {\setminus }\Sigma $$ ∂ Ω \ Σ being compact, we also give a ‘sharp’ condition for the divergence to infinity of the conformal factor near $$\Sigma $$ Σ in terms of the codimension.
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Existence and uniqueness to a fully non-linear version of the Loewner-Nirenberg problem
arXiv: Analysis of PDEs, 2018Co-Authors: María Del Mar González, Yanyan Li, Luc NguyenAbstract:We consider the problem of finding on a given Euclidean Domain $\Omega$ of dimension $n \geq 3$ a complete conformally flat metric whose Schouten curvature $A$ satisfies some equation of the form $f(\lambda(-A)) = 1$. This generalizes a problem considered by Loewner and Nirenberg for the scalar curvature. We prove the existence and uniqueness of such metric when the boundary $\partial\Omega$ is a smooth bounded hypersurface (of codimension one). When $\partial\Omega$ contains a compact smooth submanifold $\Sigma$ of higher codimension with $\partial\Omega\setminus\Sigma$ being compact, we also give a `sharp' condition for the divergence to infinity of the conformal factor near $\Sigma$ in terms of the codimension.