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| 2. |
- Bergfeldt, Aksel, et al.
(författare)
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Multilinear oscillatory integrals and estimates for coupled systems of dispersive PDEs
- 2023
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Ingår i: Transactions of the American Mathematical Society. - : AMER MATHEMATICAL SOC. - 0002-9947 .- 1088-6850. ; 376:11, s. 7555-7601
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Tidskriftsartikel (refereegranskat)abstract
- We establish sharp global regularity of a class of multilinear oscillatory integral operators that are associated to nonlinear dispersive equations with both Banach and quasi-Banach target spaces. As a consequence we also prove the (local in time) continuous dependence on the initial data for solutions of a large class of coupled systems of dispersive partial differential equations.
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| 3. |
- Bergfeldt, Aksel, et al.
(författare)
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On the regularity of multilinear Schrödinger integral operators
- 2023
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Ingår i: Analysis and Applications. - : World Scientific. - 0219-5305 .- 1793-6861. ; 21:2, s. 385-427
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Tidskriftsartikel (refereegranskat)abstract
- We prove the global regularity of multilinear Schrödinger integral operators with non-degenerate phase function that are associated to nonlinear Schrödinger equations, with Banach domain and target spaces.
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| 4. |
- Bergfeldt, Aksel, et al.
(författare)
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On the regularity of solutions to systems of dispersive partial differential equations
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We extend and improve a regularity result that shows polynomial growth in time of solutions of certain systems of PDEs that model dispersive equations interacting with a general class of multilinear operators. This is done by a multilinearisation method that extends estimates on linear oscillatory operators into properties of multilinear operators.
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| 5. |
- Bergfeldt, Aksel, et al.
(författare)
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On weighted norm inequalities for oscillatory integral operators
- 2022
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Ingår i: Analysis and Mathematical Physics. - : Springer Science and Business Media LLC. - 1664-2368 .- 1664-235X. ; 12:6
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Tidskriftsartikel (refereegranskat)abstract
- We prove weighted norm inequalities with Muckenhoupt’s Ap-weights, for a wide class of oscillatory integral operators. As a consequence, one also obtains the boundedness of commutators of the aforementioned operators with functions in BMO.
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| 6. |
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| 7. |
- Castro, Alejandro J., et al.
(författare)
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Estimates for evolutionary partial differential equations in classical function spaces
- 2023
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Ingår i: FORUM OF MATHEMATICS, SIGMA. - : Cambridge University Press. - 2050-5094. ; 11
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Tidskriftsartikel (refereegranskat)abstract
- We establish new local and global estimates for evolutionary partial differential equations in classical Banach and quasi-Banach spaces that appear most frequently in the theory of partial differential equations. More specifically, we obtain optimal (local in time) estimates for the solution to the Cauchy problem for variable-coefficient evolutionary partial differential equations. The estimates are achieved by introducing the notions of Schrodinger and general oscillatory integral operators with inhomogeneous phase functions and prove sharp local and global regularity results for these in Besov-Lipschitz and Triebel-Lizorkin spaces.
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| 8. |
- Castro, Alejandro J., et al.
(författare)
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L2-solvability of the Dirichlet, Neumann and regularity problems for parabolic equations with time-independent Hölder-continuous coefficients
- 2018
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Ingår i: Transactions of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9947 .- 1088-6850. ; 370:1, s. 265-319
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Tidskriftsartikel (refereegranskat)abstract
- We establish the L-2-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with timeindependent Holder-continuous diffusion coefficients on bounded Lipschitz domains in R-n. This is achieved through the demonstration of invertibility of the relevant layer potentials, which is in turn based on Fredholm theory and a systematic transference scheme which yields suitable parabolic Rellich-type estimates.
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| 9. |
- Castro, Alejandro, J., et al.
(författare)
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L2 Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with time-independent Hölder-continuous coefficients
- 2024
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Ingår i: Transactions of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9947 .- 1088-6850.
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Tidskriftsartikel (refereegranskat)abstract
- We establish the $L^2$-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with time-independent H\"older-continuous diffusion coefficients, on bounded Lipschitz domains in $\mathbb{R}^n$. This is achieved through the demonstration of invertibility of the relevant layer-potentials which is in turn based on Fredholm theory and a systematic transference scheme which yields suitable parabolic Rellich-type estimates.
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| 10. |
- Castro, Alejandro J., et al.
(författare)
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Regularity of Fourier integral operators with amplitudes in general Hormander classes
- 2021
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Ingår i: Analysis and Mathematical Physics. - : Springer Nature. - 1664-2368 .- 1664-235X. ; 11:3
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Tidskriftsartikel (refereegranskat)abstract
- We prove the global Lp-boundedness of Fourier integral operators that model the parametrices for hyperbolic partial differential equations, with amplitudes in classical Hormander classes S rho,delta m(Rn) for parameters 0 <= rho <= 1, 0 <= delta <1. We also consider the regularity of operators with amplitudes in the exotic class S0,m(Rn), 0 <= delta <1 and the forbidden class S,1m(Rn), 0 <= rho <= 1. Furthermore we show that despite the failure of the L2-boundedness of operators with amplitudes in the forbidden class S1,10(Rn), the operators in question are bounded on Sobolev spaces Hs(Rn) with s>0. This result extends those of Y. Meyer and E. M. Stein to the setting of Fourier integral operators.
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