# A Sufficient Condition for a Blow-Up in the Space of Absolutely Continuous Functions for the Very Weak Solution

A Sufficient Condition for a Blow-Up in the Space of Absolutely Continuous Functions for the Very... Given an open bounded smooth set $$\Omega$$ Ω in $$\mathrm{I}\!\mathrm{R}^N,\ N\geqslant 3$$ I R N , N ⩾ 3 , we provide a sufficient condition on the data $$f$$ f integrable with respect to the distance $$\delta$$ δ , to ensure the blow-up of the gradient of the very weak solution for the Dirichlet equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# A Sufficient Condition for a Blow-Up in the Space of Absolutely Continuous Functions for the Very Weak Solution

, Volume 73 (1) – Feb 1, 2016
11 pages

/lp/springer_journal/a-sufficient-condition-for-a-blow-up-in-the-space-of-absolutely-69nlJygHsi
Publisher
Springer US
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-015-9297-1
Publisher site
See Article on Publisher Site

### Abstract

Given an open bounded smooth set $$\Omega$$ Ω in $$\mathrm{I}\!\mathrm{R}^N,\ N\geqslant 3$$ I R N , N ⩾ 3 , we provide a sufficient condition on the data $$f$$ f integrable with respect to the distance $$\delta$$ δ , to ensure the blow-up of the gradient of the very weak solution for the Dirichlet equation.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Feb 1, 2016

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