Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 866 products
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QDD38 - 10/08/2008
Pagani, C.D.; Pierotti, D.
Identifiability problems of defects with Robin condition | Abstract | | We consider the inverse problem of recovering the shape of an inclusion or of a crack contained in a connected domain $ omega$, and the problem of reconstructing part of the boundary $ partial omega$ itself, when a condition of the third kind
(Robin condition) is prescribed on the defects. We prove a result of uniqueness by two measures: two different defects, with different coefficients of the Robin condition, cannot be compatible with same two pairs of Cauchy data on the (accessible) boundary. In case of cracks, we also prove that a single measure is sufficient if the coefficient of the Robin condition is known. |
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QDD37 - 10/06/2008
Bacchelli, V.
Uniqueness for the determination of unknown boundary and impedance with homogeneous Robin condition | Abstract | | We consider the problem of determining the corroded portion of the boundary of a n-dimensional body (n=2, 3) and the impedance by two measures on the accessible portion of the boundary. On the unknown boundary part it is assumed the Robin homogeneous condition.
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QDD36 - 09/08/2008
Carriero, M; Leaci, A.; Tomarelli, F.
A Dirichlet problem with free gradient discontinuity | Abstract | | We prove the existence of strong solution for Blake & Zisserman functional under Dirichlet boundary condition. The result is obtained by showing partial regularity of weak solutions up to the boundary through blow-up technique and a decay property for bi-harmonic functions in half disk. |
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QDD31 - 07/08/2008
Berchio,E.; Gazzola,F.; Pierotti,D.
Nodal solutions to critical growth elliptic problems under Steklov boundary conditions | Abstract | | We study elliptic problems at critical growth under Steklov boundary conditions in bounded
domains. For a second order problem we prove existence results for nontrivial nodal solutions. These are obtained by combining a suitable linking argument with ¯ne estimates on the concentration of Sobolev minimizers on the boundary. When the domain is the unit ball, we improve these results
by taking advantage of the explicit form of the Steklov eigenfunctions. We also partially extend
the results in the ball to the case of fourth order Steklov boundary value problems. |
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QDD35 - 07/08/2008
Cherubini, A.; Kisielewicz, A.
Collapsing words | Abstract | | Given a word $w$ over a finite alphabet $ Sigma$ and a finite
deterministic automaton $ A = < Q, Sigma, delta >$, the inequality
$| delta(Q,w)| leq |Q|-n$ means that under the natural action of
the word $w$ the image of the state set $Q$ is reduced by at least
$n$ states. A word $w$ is $n$-collapsing if this inequality holds
for any deterministic finite automaton that satisfies such an
inequality for at least one word. In this paper we prove that the
problem of recognizing $n$-collapsing words is generally
co-NP-complete, while restricted to 2-collapsing words over
2-element alphabet it belongs to P. This is connected with
introducing a new approach to collapsing words, which is shown to be
much more effective in solving various problems in the area. It
leads to interesting connections with combinatorial problems
concerning solving systems of permutation conditions on one hand,
and coloring trees with distinguished nodes on the other hand. |
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QDD34 - 06/18/2008
Gazzola, F.
No geometric approach for general overdetermined elliptic problems with nonconstant source | Abstract | | We discuss the geometric approach developed by Fragala -Gazzola-Kawohl for the study of overdetermined boundary value problems for general elliptic operators. We show that this approach does not apply when nonconstant sources are involved. |
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QDD32 - 05/13/2008
Gazzola, Filippo ; Pierotti, Dario
Positive solutions to critical growth biharmonic elliptic problems under Steklov boundary conditions | Abstract | | We study the fourth order nonlinear critical problem Delta^2u = u^{2^*-1} in the unit ball of R^n (n ge 5), subject to the Steklov boundary conditions u = Delta u-d u_{ nu}=0 on partial B.
We provide the exact range of the parameter d for which this problem admits a positive (radial) solution. We also show that the solution is unique in this range and in the class of radially symmetric functions. Finally, we study the behavior of the solution when d tends to the extremals of this range. These results complement previous results in [3]. |
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QDD33 - 05/13/2008
Gazzola, F. ; Grunau, H.C. ; Mitidieri, E.
Hardy inequalities with optimal constants and remainder terms | Abstract | | We show that the classical Hardy inequalities with optimal constants in the Sobolev spaces $W_0^{1,p}$ and in higher-order Sobolev spaces on a bounded domain $ Omega subset mathbb{R}^n$ can be refined by adding remainder terms which involve $L^p$ norms. In the higher-order case further $L^p$ norms with lower-order singular weights arise. The case $1 |
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