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Optimal regularity in the optimal switching problem
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
2016 (Engelska)Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430Artikel i tidskrift (Refereegranskat) In press
Abstract [en]

In this article we study the optimal regularity for solutions to the following weakly coupled system with interconnected obstacles{min⁡(−Δu1+f1,u1−u2+ψ1)=0min⁡(−Δu2+f2,u2−u1+ψ2)=0 arising in the optimal switching problem with two modes. We derive the optimal C1,1-regularity for the minimal solution under the assumption that the zero loop set L:={ψ1+ψ2=0} is the closure of its interior. This result is optimal and we provide a counterexample showing that the C1,1-regularity does not hold without the assumption L=L0‾. 

Ort, förlag, år, upplaga, sidor
Elsevier, 2016.
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:kth:diva-195175DOI: 10.1016/j.anihpc.2015.06.001ISI: 000389108400003Scopus ID: 2-s2.0-84939510853OAI: oai:DiVA.org:kth-195175DiVA, id: diva2:1044276
Anmärkning

QC 20161116

Tillgänglig från: 2016-11-02 Skapad: 2016-11-02 Senast uppdaterad: 2019-10-02Bibliografiskt granskad
Ingår i avhandling
1. Regularity results in free boundary problems
Öppna denna publikation i ny flik eller fönster >>Regularity results in free boundary problems
2016 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

This thesis consists of three scientific papers, devoted to the regu-larity theory of free boundary problems. We use iteration arguments to derive the optimal regularity in the optimal switching problem, and to analyse the regularity of the free boundary in the biharmonic obstacle problem and in the double obstacle problem.In Paper A, we study the interior regularity of the solution to the optimal switching problem. We derive the optimal C1,1-regularity of the minimal solution under the assumption that the zero loop set is the closure of its interior.In Paper B, assuming that the solution to the biharmonic obstacle problem with a zero obstacle is suÿciently close-to the one-dimensional solution (xn)3+, we derive the C1,-regularity of the free boundary, under an additional assumption that the noncoincidence set is an NTA-domain.In Paper C we study the two-dimensional double obstacle problem with polynomial obstacles p1 p2, and observe that there is a new type of blow-ups that we call double-cone solutions. We investigate the existence of double-cone solutions depending on the coeÿcients of p1, p2, and show that if the solution to the double obstacle problem with obstacles p1 = −|x|2 and p2 = |x|2 is close to a double-cone solution, then the free boundary is a union of four C1,-graphs, pairwise crossing at the origin.

Ort, förlag, år, upplaga, sidor
KTH: KTH Royal Institute of Technology, 2016. s. 122
Serie
TRITA-MAT-A ; 2016-10
Nationell ämneskategori
Matematik
Forskningsämne
Matematik
Identifikatorer
urn:nbn:se:kth:diva-195178 (URN)
Disputation
2016-12-02, D3, Kungl Tekniska Högskolan, Lindstedtsvägen 5, Stockholm, 13:00 (Engelska)
Opponent
Handledare
Anmärkning

QC 20161103

Tillgänglig från: 2016-11-03 Skapad: 2016-11-02 Senast uppdaterad: 2016-11-16Bibliografiskt granskad

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Aleksanyan, Gohar
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Annales de l'Institut Henri Poincare. Analyse non linéar
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