| 1. |
- Avelin, Benny, 1984-, et al.
(författare)
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Nonlinear Caldern-Zygmund Theory in the Limiting Case
- 2018
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Ingår i: Archive for Rational Mechanics and Analysis. - : Springer Science and Business Media LLC. - 0003-9527 .- 1432-0673. ; 227:2, s. 663-714
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Tidskriftsartikel (refereegranskat)abstract
- We prove a maximal differentiability and regularity result for solutions to nonlinear measure data problems. Specifically, we deal with the limiting case of the classical theory of Caldern and Zygmund in the setting of nonlinear, possibly degenerate equations and we show a complete linearization effect with respect to the differentiability of solutions. A prototype of the results obtained here tells for instance that ifwith being a Borel measure with locally finite mass on the open subset and , thenThe case is obviously forbidden already in the classical linear case of the Poisson equation.
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| 2. |
- Baroni, Paolo, et al.
(författare)
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Borderline gradient continuity of minima
- 2014
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Ingår i: Journal of Fixed Point Theory and Applications. - : Springer Science and Business Media LLC. - 1661-7738 .- 1661-7746. ; 15:2, s. 537-575
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Tidskriftsartikel (refereegranskat)abstract
- The gradient of any local minimiser of functionals of the type , where f has p-growth, p > 1, and , is continuous provided that the optimal Lorentz space condition is satisfied and is suitably Dini continuous.
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| 3. |
- Baroni, Paolo, et al.
(författare)
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Harnack inequalities for double phase functionals
- 2015
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Ingår i: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 121, s. 206-222
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Tidskriftsartikel (refereegranskat)abstract
- We prove a Harnack inequality for minimisers of a class of non-autonomous functionals with non-standard growth conditions. They are characterised by the fact that their energy density switches between two types of different degenerate phases.
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| 4. |
- Kuusi, Tuomo, et al.
(författare)
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A Boundary Harnack Inequality for Singular Equations of p-Parabolic Type
- 2014
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Ingår i: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 142:8, s. 2705-2719
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Tidskriftsartikel (refereegranskat)abstract
- We prove a boundary Harnack type inequality for nonnegative solutions to singular equations of p-parabolic type, 2n/(n+1)1,1-regular. Simple examples show, using the corresponding estimates valid for the heat equation as a point of reference, that this type of inequality cannot, in general, be expected to hold in the degenerate case ( 2
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| 5. |
- Kuusi, Tuomo, et al.
(författare)
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Sharp regularity for evolutionary obstacle problems, interpolative geometries and removable sets
- 2014
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Ingår i: Journal des Mathématiques Pures et Appliquées. - : Elsevier BV. - 0021-7824 .- 1776-3371. ; 101:2, s. 119-151
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we prove, by showing that solutions have exactly the same degree of regularity as the obstacle, optimal regularity results for obstacle problems involving evolutionary p-Laplace type operators. A main ingredient, of independent interest, is a new intrinsic interpolative geometry allowing for optimal linearization principles via blow-up analysis at contact points. This also opens the way to the proof of a removability theorem for solutions to evolutionary p-Laplace type equations. A basic feature of the paper is that no differentiability in time is assumed on the obstacle; this is in line with the corresponding linear results.
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| 6. |
- Yao, Huadong, 1982, et al.
(författare)
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Assessment of Conceptual Noise Reduction Devices for A Main Landing Gear using SNGR Method
- 2016
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Ingår i: 21st AIAA/CEAS Aeroacoustics Conference, 2015; Dallas; United States; 22 June 2015 through 26 June 2015. - Reston, Virginia : American Institute of Aeronautics and Astronautics.
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Konferensbidrag (refereegranskat)abstract
- The noise-reduction efficiencies of three conceptual designs are explored for a main landing gear (MLG) mounted on a simplified fuselage body with a bay and gear door. The designs are a fairing attached on the strut, compression of the bay space as the gear is deployed, and acoustic liners installed in the interior downstream wall of the bay. The gear door is opened in order to investigate its reflection effect on the noise during the operation. The stochastic noise generation and radiation (SNGR) method coupled with the Reynolds-averaged Navier-Stokes (RANS) equations are used for the noise prediction. This approach has the advantage to speed up the computation of both the fluid flow and noise. The Cartesian immersed boundary method (IBM) that is employed for the RANS solver further shortens the period of the overall assessment process due to fast and automatic mesh generation. The present SNGR method integrates the Lighthill analogy and the boundary element method (BEM). The Lighthill analogy is used for the prediction of the noise produced by a synthetic turbulent field that is constructed with a stochastic model based on the time-averaged turbulence quantities obtained from the RANS solution. The BEM is applied to compute the surface-scattered noise. The current fairing design is found inefficient for the noise reduction. The strategy of reducing the bay depth is not functional as well. However, the liners are effective for absorption of the acoustic pressure on the surfaces. Moreover, the noise reflection effect of the gear door is clarified. Since the horizontally projected area of the door is not negligible, the noise reflected towards the ground is found significant in the high frequency range. The conclusion is that a gear door and the way of arranging it in the gear-deployed stage should be regarded as the important factors of the product design.
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| 7. |
- Yao, Huadong, 1982, et al.
(författare)
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Assessment of Flap Side-Edge Fence Noise using SNGR Method
- 2016
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Ingår i: 21st AIAA/CEAS Aeroacoustics Conference, 2015; Dallas; United States; 22 June 2015 through 26 June 2015. - Reston, Virginia : American Institute of Aeronautics and Astronautics.
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Konferensbidrag (refereegranskat)abstract
- In this paper, the noise reduction efficiency of a flap side-edge fence is revisited and investigated using the stochastic noise generation and radiation (SNGR) method coupled with the Reynolds averaged Navier-Stokes equations (RANS). The configurations are of full scale. The baseline configuration is slotted with double flaps. The fence is attached onto both side edges of the flaps for the purpose of suppressing turbulent vortices induced by the side edge. Furthermore, the efficiency of the SNGR method is assessed as a fast prediction approach for the flap side-edge noise. The noise generation in the SNGR method employs the stochastic model to construct a synthetic turbulent field and takes advantage of the acoustic analogy to formulate the noise sources. The wave equation for the noise radiation is computed by means of the boundary element method (BEM) in frequency space. The BEM takes into account the noise scattered by the surfaces. The fences are found to be efficient for depressing the wake produced by the side edges of the double slotted flaps. Since the energetic vortices contained in the wake are the major contributor of the noise generation, the fence enable an effective noise reduction, particularly in the low frequencies below 200 Hz.
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