| 1. |
- Aleksanyan, Gohar, 1987-
(författare)
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Optimal regularity in the optimal switching problem
- 2016
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : Elsevier. - 0294-1449 .- 1873-1430. ; 33:6, s. 1455-1471
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Tidskriftsartikel (refereegranskat)abstract
- 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‾.
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| 2. |
- Ehrnström, Mats, et al.
(författare)
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On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation
- 2019
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Ingår i: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 36:6, s. 1603-1637
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Tidskriftsartikel (refereegranskat)abstract
- We consider the Whitham equation u t +2uu x +Lu x =0, where L is the nonlocal Fourier multiplier operator given by the symbol m(ξ)=tanhξ/ξ. G. B. Whitham conjectured that for this equation there would be a highest, cusped, travelling-wave solution. We find this wave as a limiting case at the end of the main bifurcation curve of P-periodic solutions, and give several qualitative properties of it, including its optimal C 1/2 -regularity. An essential part of the proof consists in an analysis of the integral kernel corresponding to the symbol m(ξ), and a following study of the highest wave. In particular, we show that the integral kernel corresponding to the symbol m(ξ) is completely monotone, and provide an explicit representation formula for it. Our methods may be generalised.
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| 3. |
- Helsing, Johan, et al.
(författare)
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Classification of spectra of the Neumann–Poincaré operator on planar domains with corners by resonance
- 2017
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Ingår i: Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 34:4, s. 991-1011
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Tidskriftsartikel (refereegranskat)abstract
- We study spectral properties of the Neumann–Poincaré operator on planar domains with corners with particular emphasis on existence of continuous spectrum and pure point spectrum. We show that the rate of resonance at continuous spectrum is different from that at eigenvalues, and then derive a method to distinguish continuous spectrum from eigenvalues. We perform computational experiments using the method to see whether continuous spectrum and pure point spectrum appear on domains with corners. For the computations we use a modification of the Nyström method which makes it possible to construct high-order convergent discretizations of the Neumann–Poincaré operator on domains with corners. The results of experiments show that all three possible spectra, absolutely continuous spectrum, singularly continuous spectrum, and pure point spectrum, may appear depending on domains. We also prove rigorously two properties of spectrum which are suggested by numerical experiments: symmetry of spectrum (including continuous spectrum), and existence of eigenvalues on rectangles of high aspect ratio.
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| 4. |
- Indrei, E., et al.
(författare)
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Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems
- 2016
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : Elsevier. - 0294-1449 .- 1873-1430. ; 33:5, s. 1259-1277
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Tidskriftsartikel (refereegranskat)abstract
- We consider fully nonlinear obstacle-type problems of the form. F(D2u,x)=f(x)a.e. in B1∩Ω,|D2u|≤Ka.e. in B1\Ω, where Ω is an open set and K>0. In particular, structural conditions on F are presented which ensure that W2,n(B1) solutions achieve the optimal C1,1(B1/2) regularity when f is Hölder continuous. Moreover, if f is positive on B-1, Lipschitz continuous, and u≠0⊂Ω, we obtain interior C1 regularity of the free boundary under a uniform thickness assumption on u=0. Lastly, we extend these results to the parabolic setting.
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| 5. |
- Shahgholian, Henrik, et al.
(författare)
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The obstacle problem with singular coefficients near Dirichlet data
- 2017
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : Elsevier. - 0294-1449 .- 1873-1430. ; 34:2, s. 293-334
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the behaviour of the free boundary close to its contact points with the fixed boundary B boolean AND {x1 = 0} in the obstacle type problem {div(x(1)(a) del u) = X-{u>0} in B+, u=0 on B boolean AND {x(1) = 0} where a < 1, B+ = B boolean AND {x(1) > 0}, B is the unit ball in R-n and n > 2 is an integer. Let Gamma = B+ boolean AND partial derivative{u > 0} be the free boundary and assume that the origin is a contact point, i.e. 0 epsilon (Gamma) over bar. We prove that the free boundary touches the fixed boundary uniformly tangentially at the origin, near to the origin it is the graph of a C-1 function and there is a uniform modulus of continuity for the derivatives of this function.
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| 6. |
- Strömqvist, Martin, 1982-
(författare)
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Harnack's Inequality for Parabolic Nonlocal Equations
- 2019
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 36:6, s. 1709-1745
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Tidskriftsartikel (refereegranskat)abstract
- The main result of this paper is a nonlocal version of Harnack's inequality for a class of parabolic nonlocal equations. We additionally establish a weak Harnack inequality as well as local boundedness of solutions. None of the results require the solution to be globally positive.
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| 7. |
- Hosseini, Vahid, 1987-, et al.
(författare)
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Microstructure and functionality of a uniquely graded super duplex stainless steel designed by a novel arc heat treatment method
- 2018
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Ingår i: Materials Characterization. - : Elsevier BV. - 1044-5803 .- 1873-4189. ; 139, s. 390-400
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Tidskriftsartikel (refereegranskat)abstract
- A novel arc heat treatment technique was applied to design a uniquely graded super duplex stainless steel (SDSS), by subjecting a single sample to a steady state temperature gradient for 10 h. A new experimental approach was used to map precipitation in microstructure, covering aging temperatures of up to 1430 °C. The microstructure was characterized and functionality was evaluated via hardness mapping. Nitrogen depletion adjacent to the fusion boundary depressed the upper temperature limit for austenite formation and influenced the phase balance above 980 °C. Austenite/ferrite boundaries deviating from Kurdjumov–Sachs orientation relationship (OR) were preferred locations for precipitation of σ at 630–1000 °C, χ at 560–1000 °C, Cr2N at 600–900 °C and R between 550 °C and 700 °C. Precipitate morphology changed with decreasing temperature; from blocky to coral-shaped for σ, from discrete blocky to elongated particles for χ, and from polygonal to disc-shaped for R. Thermodynamic calculations of phase equilibria largely agreed with observations above 750 °C when considering nitrogen loss. Formation of intermetallic phases and 475 °C-embrittlement resulted in increased hardness. A schematic diagram, correlating information about phase contents, morphologies and hardness, as a function of exposure temperature, is introduced for evaluation of functionality of microstructures.
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| 8. |
- van der Plas, Geert W., et al.
(författare)
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Distinct phases of natural landscape dynamics and intensifying human activity in the central Kenya Rift Valley during the past 1300 years
- 2019
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Ingår i: Quaternary Science Reviews. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0277-3791 .- 1873-457X. ; 218, s. 91-106
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Tidskriftsartikel (refereegranskat)abstract
- Socio-ecological stresses currently affecting the semi-arid regions of equatorial East Africa are driving environmental changes that need to be placed in a proper context of long-term human-climate-landscape interaction. Here we present a detailed reconstruction of past human influences on the landscape of the central Kenya Rift Valley, against the backdrop of natural climate-driven ecosystem dynamics over the past 1300 years. Proxy records of vegetation dynamics (pollen), animal husbandry (fungal spores), biomass burning (charcoal) and soil mobilization (clastic mineral influx) extracted from the continuous depositional archive of Lake Bogoria reveal six distinct phases of human activity. From ca 700 to 1430 CE, strong primary response of savanna woodland ecotonal vegetation to climatic moisture-balance variation suggests that anthropogenic influence on regional ecosystem dynamics was limited. The first unambiguous ecological signature of human activities involves a mid-15th century reduction of woodland/forest trees followed by the appearance of cereal pollen, both evidence for mixed farming. From the mid-17th century, animal husbandry became a significant ecological factor and reached near-modern levels by the mid-19th century, after severe early-19th century drought had substantially changed human-landscape interaction. A short-lived peak in biomass burning and evidence for soil mobilization in low-lying areas of the Bogoria catchment likely reflects the known 19th-century establishment of irrigation agriculture, while renewed expansion of forest and woodland trees reflect the return of a wetter climate and abandonment of other farmland. Since the mid-20th century, the principal signature of human activity within the Lake Bogoria catchment is the unprecedented increase in clastic sediment flux, reflecting widespread soil erosion associated with rapidly intensifying land use. (C) 2019 Elsevier Ltd. All rights reserved.
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