Regularity is a topic of the mathematical study of partial differential equations (PDE) such as Laplace's equation, about the integrability and differentiability...

In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty...

Filippis (born 1992) is an Italian mathematician whose research concerns regularity theory for elliptic partial differential equations and parabolic partial...

function Regularity conditions arise in the study of first-class constraints in Hamiltonian mechanics Regularity of an elliptic operator Regularity theory of...

In extremal graph theory, Szemerédi’s regularity lemma states that a graph can be partitioned into a bounded number of parts so that the edges between...

to the fields of calculus of variations, regularity theory of partial differential equations, and the theory of symmetrization. He is currently professor...

Statistical regularity is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough...

to nomic regularity theories, regularities manifest as laws of nature studied by science. Counterfactual theories focus not on regularities but on how...

schema, as well as the axiom of regularity (first proposed by John von Neumann), to Zermelo set theory yields the theory denoted by ZF. Adding to ZF either...

Martin Hairer's theory of regularity structures provides a framework for studying a large class of subcritical parabolic stochastic partial differential...

axiom of regularity in his axiom system. In 1931, Bernays sent a letter containing his set theory to Kurt Gödel. Gödel simplified Bernays' theory by making...

S. (2018). "Non-wellfounded Set Theory". Stanford Encyclopedia of Philosophy. Metamath page on the axiom of Regularity. Fewer than 1% of that database's...

often nonlinear and the above regularity theorem only applies to linear elliptic equations; moreover, the regularity theory for nonlinear elliptic equations...

1975, and utilised the Szemerédi regularity lemma, an essential technique in the resolution of extremal graph theory problems. A proper (vertex) coloring...

for his contributions to the fields of calculus of variations and regularity theory of partial differential equation. He is currently professor of Mathematics...

differential geometry, with a number of fundamental contributions to the regularity theory of minimal surfaces and harmonic maps. In 1976, Schoen and Shing-Tung...

vortex theory and regularity theory" 1984 Richard Melrose for "his solution of several outstanding problems in diffraction theory and scattering theory and...

Caffarelli University of Texas at Austin "For his seminal contributions to regularity theory for nonlinear partial differential equations including free-boundary...

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

principle is valid, but it requires a sophisticated application of the regularity theory for elliptic partial differential equations; see Jost and Li–Jost...

philosophy. In the philosophy of science, he is notable for developing the regularity theory of causation, which in its strongest form states that causation is...

regularity theory of the Navier−Stokes equations is, as of 2021, a well-known open problem. In the 1930s, Charles Morrey found the basic regularity theory...

The techniques used by Richard Schoen and Uhlenbeck to study the regularity theory of harmonic maps have likewise been the inspiration for the development...

Attachment theory is a psychological and evolutionary framework, concerning the relationships between humans, particularly the importance of early bonds...

Neumann pointed out that the axiom of regularity is necessary to build his theory of ordinals. The axiom of regularity was stated by von Neumann in 1925....

0 ( x ) {\displaystyle u(x,0)=u_{0}(x)} , according to parabolic regularity theory. For a nonlinear parabolic PDE, a solution of an initial/boundary-value...

theoretically sustained by a perceptually adequate formalization of visual regularity, a quantitative account of viewpoint dependencies, and a powerful form...

theorems asserting regularity of solutions outside a singular set (i.e. a closed subset of null measure) both in geometric measure theory and for variational...

earliest work aimed to develop a regularity theory for minimal hypersurfaces, changing how we view the advanced theory of minimal surfaces and calculus...

subset. In the 1980s Almgren's student Jon Pitts greatly improved the regularity theory of minimal submanifolds obtained by Almgren in the case of codimension...