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Two-microlocal regularity of quasimodes on the torus
作者：Fabricio Macià , Gabriel Rivière
来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.2111-2136MSP
摘要：We study the regularity of stationary and time-dependent solutions to strongperturbations of the free Schr\"odinger equation on two-dimensional flattori. This is achieved by performing a second microlocalizationrelated to the size of the perturbation and by analyzing concentratio...
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    Quantitative stochastic homogenization and regularity theory of parabolic equations
    作者：Scott Armstrong , Alexandre Bordas , Jean-Christophe Mourrat
    来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.1945-2014MSP
    摘要：We develop a quantitative theory of stochastic homogenization for linear,uniformly parabolic equations with coefficients depending on space andtime. Inspired by recent works in the elliptic setting, our analysisis focused on certain subadditive quantities derived from a variation...
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      Invariant measure and long time behavior ofregular solutions of the Benjamin–Ono equation
      作者：Mouhamadou Sy
      来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.1841-1879MSP
      摘要：The Benjamin--Ono equation describes the propagation of internal wavesin a stratified fluid. In the present work, we study large time dynamicsof its regular solutions via some probabilistic point of view. We provethe existence of an invariant measure concentrated on $C^\infty(\ma...
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        Spectral distribution of the free Jacobi process, revisited
        作者：Tarek Hamdi
        来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.2137-2148MSP
        摘要：We obtain a description for the spectral distribution of the free Jacobiprocess for any initial pair of projections. This result relies on a studyof the unitary operator $RU_tSU_t^*$, where$R,S$ are two symmetries and $(U_t)_{t\geq0}$ is a free unitary Brownianmotion, freely inde...
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          On weak weighted estimates of the martingale transform and a dyadic shift
          作者：Fedor Nazarov , Alexander Reznikov , Vasily Vasyunin ...
          来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.2089-2109MSP
          摘要：We consider weak-type estimates for several singular operators using theBellman-function approach. In particular, we consider a concrete dyadicshift. We disprove the $A_1$ conjecture for those operators, whichstayed open after Muckenhoupt andWheeden's conjecture was disproved by ...
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            Monotonicity of nonpluripolar products andcomplex Monge–Ampère equations with prescribed singularity
            作者：Tamás Darvas , Eleonora Di Nezza , Chinh H. Lu
            来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.2049-2087MSP
            摘要：We establish the monotonicity property for the mass of nonpluripolarproducts on compact K\"ahler manifolds, and we initiate the study of complexMonge--Amp\`ere-type equations with prescribed singularity type. Using thevariational method ofBerman, Boucksom, Guedj and Zeriahi we pr...
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              Propagation and recovery of singularities in the inverse conductivity problem
              作者：Allan Greenleaf , Matti Lassas , Matteo Santacesaria ...
              来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.1901-1943MSP
              摘要：The ill-posedness of Calder\'on's inverse conductivity problem,responsible for the poor spatial resolution of electrical impedance tomography(EIT), has been an impetus forthe development of hybrid imaging techniques, which compensate for thislack of resolution by coupling with as...
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                Hopf potentials for the Schrödingeroperator
                作者：Luigi Orsina , Augusto C. Ponce
                来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.2015-2047MSP
                摘要：We establish the Hopf boundary point lemma for the Schr\"odinger operator$-\Delta + V$ involving potentials~$V$ that merely belong to the space$L^{1}_{\operatorname{loc}}(\Omega)$.More precisely, we prove that among all nonnegative supersolutions $u$of $-\Delta + V$ which vanish ...
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                  Rigidity of minimizers in nonlocal phase transitions
                  作者：Ovidiu Savin
                  来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.1881-1900MSP
                  摘要：We obtain the classification of certain global bounded solutions forsemilinear nonlocal equations of the~type\[\triangle^{\mskip-2mu s} u=W'(u) \quad \mbox{in } \R^n, \quad \mbox{with } s \in \bigl(\tfrac12 ,1\bigr),\]where $W$ is a double-well potential.
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                    Multiple crack damage detection of structures using simplified PZT model
                    作者：Narayanan Jinesh , Krishnapillai Shankar
                    来源：[J].Journal of Mechanics of Materials and Structures(IF 0.46), 2018, Vol.13 (2), pp.225-246MSP
                    摘要：A novel damage identification scheme for multiple cracks in beams ispresented based on the one-dimensional (1-D) piezoelectric patch withbeam model. A hybrid element constituted of a 1-D beam element anda PZT sensor is used with reduced material properties. This modelismore conve...
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