Parabolic equations with rough data

Numerical Schemes for Rough Parabolic Equations

A discrete approach to Rough Parabolic Equations

By combining the formalism of [8] with a discrete approach close to the considerations of [6], we interpret and we solve the rough partial differential equation d yt = Ayt d t + ∑m i=1 fi(yt) d x i t (t ∈ [0, T]) on a compact domain O of R, where A is a rather general elliptic operator of L(O ) (p > 1), fi(φ)(ξ) := fi(φ(ξ)) and x is the generator of a 2-rough path. The (global) existence, uniqu...

Existence of Solutions for Degenerate Parabolic Equations with Rough Coefficients

We prove that a sequence of quasi-solutions to non-degenerate degenerate parabolic equations with rough coefficients is strongly Lloc-precompact. The result is obtained using the H-measures and a new concept of quasihomogeneity. A consequence of the precompactness is existence of a weak solution to the equation under consideration.

Hölder-estimates for non-autonomous parabolic problems with rough data

In this paper we establish Hölder estimates for solutions to non-autonomous parabolic equations on non-smooth domains which are complemented with mixed boundary conditions. The corresponding elliptic operators are of divergence type, the coefficient matrix of which depends only measurably on time. These results are in the tradition of the classical book of Ladyshenskaya et al. [39], which also ...

Slack-Based Measurement with Rough Data

Rough data envelopment analysis (RDEA) evaluates the performance of the decision making units (DMUs) under rough uncertainty assumption. In this paper, new discussion regarding RDEA is extended. The RSBM model is proposed by integrating SBM model and rough set theory. The process of reaching solution is presented and this model is applied to efficiency evaluation of the DMUs with uncertain ...