scholarly journals Non-local approximation of free-discontinuity problems with linear growth

2007 ◽  
Vol 13 (1) ◽  
pp. 135-162 ◽  
Author(s):  
Luca Lussardi ◽  
Enrico Vitali
Keyword(s):  
Linear Growth ◽  
Local Approximation ◽  
Free Discontinuity Problems ◽  
Non Local

scholarly journals On some non-local approximation of nonisotropic Griffith-type functionals$ ^\dagger $

2021 ◽  
Vol 4 (4) ◽  
pp. 1-22
Author(s):  
Fernando Farroni ◽  
◽  
Giovanni Scilla ◽  
Francesco Solombrino ◽  
Keyword(s):  
Sobolev Spaces ◽  
Local Approximation ◽  
Convolution Type ◽  
Gamma Convergence ◽  
Non Local ◽  
Suitable Sequence

<abstract><p>The approximation in the sense of $ \Gamma $-convergence of nonisotropic Griffith-type functionals, with $ p- $growth ($ p &gt; 1 $) in the symmetrized gradient, by means of a suitable sequence of non-local convolution type functionals defined on Sobolev spaces, is analysed.</p></abstract>

scholarly journals Finite-difference approximation of free-discontinuity problems

2001 ◽  
Vol 131 (3) ◽  
pp. 567-595 ◽  
Author(s):  
Massimo Gobbino ◽  
Maria Giovanna Mora
Keyword(s):  
Finite Difference ◽  
Finite Differences ◽  
Pointwise Convergence ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Compactness Result ◽  
Free Discontinuity Problems ◽  
Non Local ◽  
Γ Convergence

We approximate functionals depending on the gradient of u and on the behaviour of u near the discontinuity points by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, Γ-convergence and a compactness result, which implies, in particular, the convergence of minima and minimizers.

Theory of dissociative recombination and related processes

1974 ◽  
Vol 340 (1622) ◽  
pp. 301-322 ◽  
Keyword(s):  
Energy Spectrum ◽  
Cross Section ◽  
Dissociative Recombination ◽  
Resonance State ◽  
Local Approximation ◽  
Operator Technique ◽  
Final State ◽  
Projection Operator Technique ◽  
Non Local ◽  
Associative Ionization

The theory of dissociative recombination (and the closely related processes of associative ionization and mutual quenching) is developed by using the Feshbach projection operator technique. An expression is given for the cross-section into a specific final state of the dissociating atoms. It is found that the complex potential energy corresponding to a resonance state is non-local in nature and the implications of using a local approximation are considered. The theory of photodissociation through resonances is developed with special reference to the energy spectrum of the products. It is shown that dissociative attachment can be studied without explicitly constructing the intermediate state.

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