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...
 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...
 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 $C^\infty(\ma...  作者：Tarek Hamdi 来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.2137-2148MSP 摘要：We obtain a description for the spectral distribution of the free Jacobiprocess for any initial pair of projections. This result relies on a studyof the unitary operator$RU_tSU_t^*$, where$R,S$are two symmetries and$(U_t)_{t\geq0}$is a free unitary Brownianmotion, freely inde...  作者：Fedor Nazarov , Alexander Reznikov , Vasily Vasyunin ... 来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.2089-2109MSP 摘要：We consider weak-type estimates for several singular operators using theBellman-function approach. In particular, we consider a concrete dyadicshift. We disprove the$A_1$conjecture for those operators, whichstayed open after Muckenhoupt andWheeden's conjecture was disproved by ...  作者：Tamás Darvas , Eleonora Di Nezza , Chinh H. Lu 来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.2049-2087MSP 摘要：We establish the monotonicity property for the mass of nonpluripolarproducts on compact K\"ahler manifolds, and we initiate the study of complexMonge--Amp\`ere-type equations with prescribed singularity type. Using thevariational method ofBerman, Boucksom, Guedj and Zeriahi we pr...  作者：Allan Greenleaf , Matti Lassas , Matteo Santacesaria ... 来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.1901-1943MSP 摘要：The ill-posedness of Calder\'on's inverse conductivity problem,responsible for the poor spatial resolution of electrical impedance tomography(EIT), has been an impetus forthe development of hybrid imaging techniques, which compensate for thislack of resolution by coupling with as...  作者：Luigi Orsina , Augusto C. Ponce 来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.2015-2047MSP 摘要：We establish the Hopf boundary point lemma for the Schr\"odinger operator$-\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$which vanish ...  作者：Ovidiu Savin 来源：[J].Analysis & PDE, 2018, Vol.11 (8), pp.1881-1900MSP 摘要：We obtain the classification of certain global bounded solutions forsemilinear nonlocal equations of the~type$\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.
 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...