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[KNIHA][B] Shape variation and optimization
A Henrot, M Pierre - 2018 - ems.press
Optimizing the shape of an object to make it the most efficient or the most resistant or the
most streamlined or the lightest or the most noiseless or the most stealthy or the cheapest is …
most streamlined or the lightest or the most noiseless or the most stealthy or the cheapest is …
Variational problems with two phases and their free boundaries
The problem of minimizing $\int {[\nabla\upsilon {|^ 2}}+{q^ 2}(x){\lambda^ 2}(\upsilon)] dx $
in an appropriate class of functions $\upsilon $ is considered. Here $ q (x)\ne 0$ and …
in an appropriate class of functions $\upsilon $ is considered. Here $ q (x)\ne 0$ and …
Variational problems with free boundaries for the fractional Laplacian
We discuss properties (optimal regularity, non-degeneracy, smoothness of the free
boundary...) of a variational interface problem involving the fractional Laplacian; Due to the …
boundary...) of a variational interface problem involving the fractional Laplacian; Due to the …
An optimal design problem with perimeter penalization
We study the optimal design problem of finding the minimal energy configuration for a
mixture of two conducting materials when a perimeter penalization of the unknown domain …
mixture of two conducting materials when a perimeter penalization of the unknown domain …
The state of the art for a conjecture of De Giorgi and related problems
A Farina, E Valdinoci - Recent progress on reaction-diffusion …, 2009 - books.google.com
→ R Given a function v: R"→ R and kЄ N, with k≤ n, we say that v is k-dimensional (or, for
short, kD) if there exists a function v.: Rk in such a way that, after a suitable rotation of the …
short, kD) if there exists a function v.: Rk in such a way that, after a suitable rotation of the …
[HTML][HTML] Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes
M Cozzi - Journal of Functional Analysis, 2017 - Elsevier
We study energy functionals obtained by adding a possibly discontinuous potential to an
interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that …
interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that …
[KNIHA][B] Optimization of elliptic systems: theory and applications
P Neittaanmaki, J Sprekels, D Tiba - 2007 - books.google.com
The present monograph is intended to provide a comprehensive and accessible introduction
to the optimization of elliptic systems. This area of mathematical research, which has many …
to the optimization of elliptic systems. This area of mathematical research, which has many …
Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type
GQ Chen, M Feldman - Journal of the American Mathematical Society, 2003 - ams.org
We establish the existence and stability of multidimensional transonic shocks for the Euler
equations for steady potential compressible fluids. The Euler equations, consisting of the …
equations for steady potential compressible fluids. The Euler equations, consisting of the …
Stochastic interface models
T Funaki - Lectures on probability theory and statistics, 1869 - Springer
In these notes we try to review developments in the last decade of the theory on stochastic
models for interfaces arising in two phase system, mostly on the so-called∇ ϕ interface …
models for interfaces arising in two phase system, mostly on the so-called∇ ϕ interface …
[PDF][PDF] A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on
LA Caffarelli - Annali della Scuola Normale Superiore di Pisa-Classe …, 1988 - numdam.org
In this third part of our work on regularity of free boundaries we will show the existence of
weak solutions to the Dirichlet problem. In the meantime, we will have to develop …
weak solutions to the Dirichlet problem. In the meantime, we will have to develop …