Sentence examples for boundary regularity from inspiring English sources
We establish sharp interior and boundary regularity estimates for solutions to ∂tu−Lu= f t,x) in I×Ω, with I⊂R and Ω⊂Rn.
Our argument also relies on suitable extension techniques and on an estimate on the decay of the eigenfunctions at the boundary which could be interpreted as a boundary regularity result.
The role of the exponent N+1N−1 (first discovered by Brezis and Turner [H. Brezis, R. Turner, On a class of superlinear elliptic problems, Comm. Partial Differential Equations 2 (1977) 601 614]) for boundary regularity, parallels that of NN−2 for interior singularities.
Besides, the following boundary regularity results are well known.
Existence, boundary regularity, uniqueness, and comparison results are established.
We study the boundary regularity of weak solutions to nonlinear obstacle problem with -obstacle function, and obtain the boundary regularity.
Joyce and Craig Cachopa are now finding the boundary with regularity, as Lancashire set a bold field in a bid to force a victory.
Nightwatchman Mishra, who had served notice of his batting ability with a breezy 43 in the first innings, started to find the boundary with regularity, taking the partnership past fifty with a flick to the midwicket fence.
Reprieved, Amla continued to find the boundary with regularity as he and Jacques Kallis added 28 from the last 15 balls - including 18 off a Stuart Broad over - to carry South Africa to a competitive total.
"Chris Jordan quickly removed Adam Lyth for three and Alex Lees fell to Lewis Hatchett for 29, but then Gary Ballance and Andrew Gale scored freely in an unbroken 51-run partnership in which they both found the boundary with regularity". Mark Footitt bowled an inspired new-ball spell in what is likely to be his final Championship appearance for Derbyshire.
Grotowski obtained boundary partial regularity results for more general systems: − D α A i α ( ⋅, u, D u ) = f i ( ⋅, u, D u ), i = 1, …, N. In this paper, we extend the results in [9].
