Small Perturbation Solutions for Elliptic Equations

By Ovidiu Savin. 2007

207 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d579303fb8f488c30eb8725ecd00cdefcd50b35e

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Unique Continuation for Fractional Orders of Elliptic Equations (2016, methodology): “This was recently generalized to fully nonlinear uniformly elliptic equations of second order by Armstrong-Silvestre [3] through a perturbative technique by Savin [25].”
Regularity for parabolic integro-differential equations with very irregular kernels (2014, methodology): “Rather, we circumvent the often-used gradient mapping of the convex envelop by using a mapping which associates points via their correspondence through parameters in an inf-convolution, modeled on the arguments of [21], originating in [9], [31].”
Partial regularity of solutions of fully nonlinear, uniformly elliptic equations (2011, methodology): “1 here, following the argument of [10].”
Upper bounds for parabolic equations and the Landau equation (2015, methodology): “We use a modern approach which consist in estimating the measure of points where f can be touched from above with certain quadratic polynomials (see [11] and [14] for examples of the use of this approach to obtain estimates for equations in nondivergence form).”
Estimates on elliptic equations that hold only where the gradient is large (2013, methodology): “lman-Pucci estimate. Here, we proceed diﬀerently by estimating directly the measure of the set of points where the super-solution can be touched by cusps from below. This idea was inspired by [4] and [16], where a similar argument is carried out with paraboloids instead of cusps. We strongly believe”
Nonlocal minimal surfaces (2009, methodology): “The normal velocity at a point x0 ∈ S satisfies”
$$C^{2,\alpha }$$C2,α estimates for nonlinear elliptic equations in complex and almost complex geometry (2014, methodology): “This PDE theorem is a consequence of results of Caffarelli [3] and ideas adapted from the work of the second-named author [65] (see also [49]).”