A new regularity theorem for bang-bang trajectories

2006 ◽  
pp. 199-211 ◽  
Author(s):  
H. J. Sussmann
Keyword(s):  
Regularity Theorem

Boundary conditions for zero‐rest‐mass fields in curved space‐time: A regularity theorem

1981 ◽  
Vol 22 (5) ◽  
pp. 1081-1083 ◽  
Author(s):  
James L. Anderson ◽  
Ronald E. Kates
Keyword(s):  
Boundary Conditions ◽  
Rest Mass ◽  
Space Time ◽  
Regularity Theorem ◽  
Curved Space

A partial regularity theorem for harmonic maps at a free boundary

1989 ◽  
Vol 2 (4) ◽  
pp. 299-343 ◽  
Author(s):  
Frank Duzaar ◽  
Klaus Steffen
Keyword(s):  
Free Boundary ◽  
Partial Regularity ◽  
Harmonic Maps ◽  
Regularity Theorem

A Regularity Theorem for a Singular Elliptic Equation

1983 ◽  
Vol 14 (3) ◽  
pp. 223-236 ◽  
Author(s):  
P. D. Smith ◽  
Murray H. Protter
Keyword(s):  
Elliptic Equation ◽  
Regularity Theorem ◽  
Singular Elliptic Equation

scholarly journals On algebra with universal finite module of differentials

1981 ◽  
Vol 83 ◽  
pp. 107-121 ◽  
Author(s):  
Norio Yamauchi
Keyword(s):  
Local Ring ◽  
Positive Characteristic ◽  
Regularity Theorem ◽  
Local Case ◽  
Finite Module ◽  
Characteristic Case ◽  
Differential Modules ◽  
Module Of Differentials

Let k be a field and A a noetherian k-algebra. In this note, we shall study the universal finite module of differentials of A over k, which is denoted by Dk(A). When the characteristic of k is zero, detailed results have been obtained by Scheja and Storch [8]. So we shall treat the positive characteristic case. In § 1, we shall study differential modules of a local ring over subfields. We obtain a criterion of regularity (Theorem (1.14)). In § 2, we shall study the formal fibres and regular locus of A with Dk(A). Our main result is Theorem (2.1) which shows that, if Dk(A) exists, then A is a universally catenary G-ring under a certain assumption. In the local case, this is a generalization of Matsumura’s theorem ([5] Theorem 15), where regularity of A is assumed.

scholarly journals Regularity of area minimizing currents mod p

2020 ◽  
Vol 30 (5) ◽  
pp. 1224-1336
Author(s):  
Camillo De Lellis ◽  
Jonas Hirsch ◽  
Andrea Marchese ◽  
Salvatore Stuvard
Keyword(s):  
Hausdorff Dimension ◽  
Partial Regularity ◽  
Singular Set ◽  
Regularity Theorem ◽  
Locally Finite ◽  
Dimensional Measure ◽  
Area Minimizing ◽  
Mod P

AbstractWe establish a first general partial regularity theorem for area minimizing currents $${\mathrm{mod}}(p)$$ mod ( p ) , for every p, in any dimension and codimension. More precisely, we prove that the Hausdorff dimension of the interior singular set of an m-dimensional area minimizing current $${\mathrm{mod}}(p)$$ mod ( p ) cannot be larger than $$m-1$$ m - 1 . Additionally, we show that, when p is odd, the interior singular set is $$(m-1)$$ ( m - 1 ) -rectifiable with locally finite $$(m-1)$$ ( m - 1 ) -dimensional measure.

scholarly journals The free-boundary Brakke flow

2020 ◽  
Vol 2020 (758) ◽  
pp. 95-137 ◽  
Author(s):  
Nick Edelen
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Monotonicity Formula ◽  
Local Regularity ◽  
Regularity Theorem ◽  
Elliptic Regularization ◽  
Barrier Surface ◽  
Boundary Mean Curvature

AbstractWe develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must “pop” upon tangential contact with the barrier. We prove a compactness theorem for free-boundary Brakke flows, define a Gaussian monotonicity formula valid at all points, and use this to adapt the local regularity theorem of White [23] to the free-boundary setting. Using Ilmanen’s elliptic regularization procedure [10], we prove existence of free-boundary Brakke flows.

scholarly journals Wave Front Sets with respect to the Iterates of an Operator with Constant Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
C. Boiti ◽  
D. Jornet ◽  
J. Juan-Huguet
Keyword(s):  
Differential Operator ◽  
Wave Front ◽  
Partial Differential Operator ◽  
Regularity Theorem ◽  
Wave Front Set ◽  
Open Set ◽  
Wave Front Sets ◽  
Constant Coefficients ◽  
New Type ◽  
Classical Distribution

We introduce the wave front setWF*P(u)with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distributionu∈𝒟′(Ω)in an open set Ω in the setting of ultradifferentiable classes of Braun, Meise, and Taylor. We state a version of the microlocal regularity theorem of Hörmander for this new type of wave front set and give some examples and applications of the former result.

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