THE DISCONTINUITY PROBLEM

2022 ◽  
pp. 1-22
Author(s):  
VASCO BRATTKA
Keyword(s):  
Discontinuity Problem

On Discontinuity Problem at Fixed Point

2018 ◽  
Vol 43 (1) ◽  
pp. 499-517 ◽  
Author(s):  
R. P. Pant ◽  
Nihal Yilmaz Özgür ◽  
Nihal Taş
Keyword(s):  
Fixed Point ◽  
Discontinuity Problem

FREE DISCONTINUITY PROBLEMS WITH UNBOUNDED DATA

1994 ◽  
Vol 04 (06) ◽  
pp. 843-855 ◽  
Author(s):  
ANTONIO LEACI
Keyword(s):  
Pattern Recognition ◽  
Surface Energy ◽  
Variational Problem ◽  
Mathematical Physics ◽  
Closed Set ◽  
Free Discontinuity Problems ◽  
Volume Energy ◽  
Discontinuity Problem

We prove the existence of a minimizing pair for a free discontinuity problem, i.e. a variational problem in which the unknowns are a closed set K and a function suitably smooth outside K. Examples of such problems come from pattern recognition and mathematical physics, when both “volume” energy and “surface” energy are present.

Prices, Sanctions, and Discontinuities

2014 ◽  
Author(s):  
Robert D. Cooter ◽  
Ariel Porat
Keyword(s):  
Standard Of Care ◽  
Tort Law ◽  
Contract Law ◽  
Standards Of Care ◽  
Lack Of Information ◽  
Discontinuity Problem ◽  
Negligence Law

This chapter considers a misalignment between the standards of care and damages due to a court's lack of information regarding causation. It first explains the distinction between prices and sanctions before discussing the discontinuity problem in tort law and contract law. It then examines how, under negligence law, an injurer who fails to satisfy the standard of care is liable for the harm caused by his negligence and how courts impose liability on the slightly negligent injurer for all harms caused by his behavior. It also explores how discontinuity in liability under negligence law creates misalignments that may result in overdeterrence or underdeterrence. The chapter concludes by suggesting how these misalignments could be mitigated.

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