Weakly Differentiable Functions

By Otmar Scherzer, Markus Grasmair, H. Grossauer, Markus Haltmeier, Frank Lenzen. 2009

703 citations recorded by the source corpus.

Subfields: Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/472f9a9a1ae50223d79fb13f92058c421d0ed754

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “There are many well-known textbooks on Sobolev spaces, among which we mention here only the monographs [3, 5, 164, 136, 284, 291, 351, 569, 584, 744, 783].”
Simplicity of the principal eigenvalue for indefinite quasilinear problems (2007, methodology): “2, [32]] to the functions log ( 1 + u δ ) and by using (3.”
Heat Equation with Dynamical Boundary Conditions of Reactive Type (2008, background): “Unfortunately, (u, v) = ∫ Ω ∇u∇v is only a pseudo–scalar product on H(Ω), so we look for a suitable subspace of H(Ω), which has to contain all but finitely many eigenfunctions of A and in which (·, ·) is a scalar product, that is to say where a Poincaré type inequality holds (see [30]).”
Higher-order Sobolev embeddings and isoperimetric inequalities (2013, background): “where ∂E denotes the essential boundary of E, in the sense of geometric measure theory [70,92].”
The Monge-Ampµere equation and its geometric applications (2008, background): “Then at any point x ∈ Ω where u is twice differentiable, D(2)uh(x) → ∂(2)u(x) [Zi].”
Bracketing Metric Entropy Rates and Empirical Central Limit Theorems for Function Classes of Besov- and Sobolev-Type (2007, background): “5 in [40], the essential total variation of every such f is finite.”
A singularly perturbed Kirchhoff problem revisited (2016, methodology): “For the properties of the Sobolev functions, we refer to the monograph [37].”
Well-posedness for the drift-diffusion system in Lp arising from the semiconductor device simulation (2008, background): “For the proof see Stein [23], Ziemer [26].”
Suppression of Chemotactic Explosion by Mixing (2015, methodology): “3) follows from the well known properties of Ḣ 1 functions under Lipschitz transformations of coordinates [40].”
Non-Gaussian statistical inverse problems. Part I: Posterior distributions (2012, background): “2 in [148]), and the mapping is actually onto the subspace H = {f ∈ H(1)(0, 1) : f(0) = 0}.”
Uniform central limit theorems for kernel density estimators (2008, background): “If DαwT f (·) is, for every α with |α| = 1, also a ’regular’ distribution given by another locally integrable function g (or, alternatively, by a signed Borel measureµ), then we say that g (resp.µ) is the weak derivative of f , and we write g = Dαw f (µ = Dαw f ); cf., e.g., p.42 in Ziemer [33].”