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Displaying similar documents to “On the zero-temperature or vanishing viscosity limit for certain Markov processes arising from Lagrangian dynamics”

Hamilton-Jacobi flows and characterization of solutions of Aronsson equations

Petri Juutinen, Eero Saksman (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this note, we verify the conjecture of Barron, Evans and Jensen [3] regarding the characterization of viscosity solutions of general Aronsson equations in terms of the properties of associated forward and backwards Hamilton-Jacobi flows. A special case of this result is analogous to the characterization of infinity harmonic functions in terms of convexity and concavity of the functions r ↦ max y ∈ B r ( x ) u ( y ) and r ↦ min y ∈ B r ( x ) u ( y ) , respectively.

Widom factors for the Hilbert norm

Gökalp Alpan, Alexander Goncharov (2015)

Banach Center Publications

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Given a probability measure μ with non-polar compact support K, we define the n-th Widom factor W²ₙ(μ) as the ratio of the Hilbert norm of the monic n-th orthogonal polynomial and the n-th power of the logarithmic capacity of K. If μ is regular in the Stahl-Totik sense then the sequence ( W ² ₙ ( μ ) ) n = 0 ∞ has subexponential growth. For measures from the Szegő class on [-1,1] this sequence converges to some proper value. We calculate the corresponding limit for the measure that generates the Jacobi polynomials,...

Concentration in the Nonlocal Fisher Equation: the Hamilton-Jacobi Limit

Benoît Perthame, Stephane Génieys (2010)

Mathematical Modelling of Natural Phenomena

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The nonlocal Fisher equation has been proposed as a simple model exhibiting Turing instability and the interpretation refers to adaptive evolution. By analogy with other formalisms used in adaptive dynamics, it is expected that concentration phenomena (like convergence to a sum of Dirac masses) will happen in the limit of small mutations. In the present work we study this asymptotics by using a change of variables that leads to a constrained Hamilton-Jacobi equation. We prove the convergence...