Inverse problems for the fractional-Laplacian with lower order non-local perturbations

[1]  Zhi-Ming Ma,et al.  Reflected Symmetric α-Stable Processes and Regional Fractional Laplacian , 2006 .

[2]  A. Calderón,et al.  On an inverse boundary value problem , 2006 .

[3]  R. Temam.  Navier-Stokes Equations , 1977 .

[4]  Xavier Ros-Oton,et al.  Nonlocal problems with Neumann boundary conditions , 2014, 1407.3313.

[5]  A. Ponce.  Elliptic Pdes, Measures and Capacities: From the Poisson Equation to Nonlinear Thomas-fermi Problems , 2016 .

[6]  Huyuan Chen.  The Dirichlet elliptic problem involving regional fractional Laplacian , 2015, Journal of Mathematical Physics.

[7]  Gerd Grubb,et al.  Local and nonlocal boundary conditions for μ-transmission and fractional elliptic pseudodifferential operators , 2014, 1403.7140.

[8]  W. McLean.  Strongly Elliptic Systems and Boundary Integral Equations , 2000 .

[9]  Mikko Salo,et al.  The fractional Calderón problem: Low regularity and stability , 2017, Nonlinear Analysis.

[10]  David Applebaum,et al.  Lévy Processes and Stochastic Calculus by David Applebaum , 2009 .

[11]  E. Valdinoci,et al.  Hitchhiker's guide to the fractional Sobolev spaces , 2011, 1104.4345.

[12]  M. Kwasnicki,et al.  Ten equivalent definitions of the fractional laplace operator , 2015, 1507.07356.

[13]  Gunther Uhlmann,et al.  Uniqueness and reconstruction for the fractional Calderón problem with a single measurement , 2018, Journal of Functional Analysis.

[14]  Antti V. Vähäkangas,et al.  On improved fractional Sobolev–Poincaré inequalities , 2013, 1312.5118.

[15]  Kai Lai Chung,et al.  From Brownian Motion To Schrödinger's Equation , 1995 .

[16]  R. Temam,et al.  Navier-Stokes equations: theory and numerical analysis: R. Teman North-Holland, Amsterdam and New York. 1977. 454 pp. US $45.00 , 1978 .

[17]  Zhi-Ming Ma,et al.  BOUNDARY PROBLEMS FOR FRACTIONAL LAPLACIANS , 2005 .

[18]  N. S. Landkof.  Foundations of Modern Potential Theory , 1972 .

[19]  José M. Mazón,et al.  Nonlocal Diffusion Problems , 2010 .

[20]  On fractional Poincar\'e inequalities , 2011 .

[21]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[22]  Gunther Uhlmann,et al.  The Calderón problem for the fractional Schrödinger equation , 2016, 1609.09248.

[23]  Gunther Uhlmann,et al.  Inverse problems: seeing the unseen , 2014 .

[24]  D. Applebaum.  Lévy Processes and Stochastic Calculus: Preface , 2009 .

[25]  L. Tartar.  An Introduction to Sobolev Spaces and Interpolation Spaces , 2007 .

[26]  Yi-Hsuan Lin,et al.  The Calderón problem for variable coefficients nonlocal elliptic operators , 2017, 1708.00654.

[27]  Ritva Hurri-Syrjänen,et al.  On fractional Poincaré inequalities , 2013 .

[28]  Bartłomiej Dyda,et al.  A fractional order Hardy inequality , 2004 .

[29]  E. Valdinoci,et al.  Nonlocal Diffusion and Applications , 2015, 1504.08292.