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Displaying 181 – 200 of 2105

A uniqueness property for measures on $C^{n}$

Chalice, Donald R. (1975)

Portugaliae mathematica

A uniqueness result for the continuity equation in two dimensions

Giovanni Alberti, Stefano Bianchini, Gianluca Crippa (2014)

Journal of the European Mathematical Society

We characterize the autonomous, divergence-free vector fields $b$ on the plane such that the Cauchy problem for the continuity equation $\partial_{t} u + \frac{.}{\dot{}} (b u) = 0$ admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential $f$ associated to $b$ . As a corollary we obtain uniqueness under the assumption that the curl of $b$ is a measure. This result can be extended to certain non-autonomous vector fields $b$ with bounded divergence....

A universal null graph whose domain has positive measure

G. V. Cox (1982)

Colloquium Mathematicae

A Variational Principle for the Hausdorff Dimension of Fractal Sets.

C.D. Cutler, L. Olsen (1994)

Mathematica Scandinavica

A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies

Alice Fiaschi (2009)

ESAIM: Control, Optimisation and Calculus of Variations

Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution in terms...