What does the term "regularity" mean? - Mathematics Stack …
2015年8月23日 · The regularity a solution can inherit depends on the properties of the problem, i.e., the smoothness of a domain boundary, the smoothness of boundary conditions and initial data. Notice here that the smoothness of the initial data falls …
regularity of a measure - Mathematics Stack Exchange
Help save this proof about the regularity of the lebesgue measure on $\mathbb{R}^d$ 0 An example of a measure and of a set s.t. its measure cannot be approximated by measures of its open subsets
set theory - Help understanding the axiom of regularity
2019年10月6日 · Usual mathematical results (like propositions on analysis and geometry) would not need the axiom of regularity, but some deeper set theory heavily relies on the axiom of regularity. As a side note, a regularity-free proof of "the existence of a basis on any vector spaces implies AC" is not known. $\endgroup$ –
real analysis - Definition of regularity in PDE theory - Mathematics ...
2017年7月26日 · Furthermore, the issue of regularity is often isolated in proofs, so e.g. if you want to prove existence and uniqueness of a classical solution (i.e. "strongly" differentiable function that actually satisfies a PDE in exactly the way that it is posed) to a PDE, you first show existence and uniqueness of a weak solution which is often much ...
logic - How does the axiom of regularity make sense?
2017年5月18日 · The axiom of regularity is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. I'm sure I'm grossly misunderstanding this, but it doesn't seem to make any sense.
real analysis - Help save this proof about the regularity of the ...
2019年1月10日 · In a previous homework our task was to prove the regularity of the Lebegue-measure on $\mathbb{R}^d$. More precisely: More precisely: Let $(\mathbb{R}^d, \mathcal{M}^*, \lambda)$ be a measure space and $\mathcal{M}^* := \mathcal{M}^*(\mathbb{R}^d)$ be the $\sigma$ -algebra of the $\lambda^*$ -measurable sets, with $\lambda$ being the by the ...
On the "regularity" of the boundary of an open set
I'm considering the following regularity conditions for the boundary of $\Omega$: $\overline{\Omega}$ is a topological manifold with boundary (in other words, around each boundary point, $\Omega$ looks like a Euclidean half-space --up to homeomorphism).
algebraic geometry - Regularity vs smoothness in positive ...
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Need good reference or a proof on regularity of solution to …
The only reference I am aware of which gives a proof of this result, is the textbook by Mikhailov [1]. Precisely, he deals with the regularity problem for the first boundary problem (Dirichlet problem) and the second boundary problem (Neumann problem) for the Poisson equation in …
set theory - Axiom of Regularity - Mathematics Stack Exchange
I am having difficulty understanding Axiom of Regularity : Every non-empty set $\\rm A$ contains an element $\\rm B$ which is disjoint from $\\rm A.$ So from my understanding if I have a set like:...