Titlebook: Contemporary Research in Elliptic PDEs and Related Topics; Serena Dipierro Book 2019 Springer Nature Switzerland AG 2019 Partial different

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,Maximum Principles at Infinity and the Ahlfors-Khas’minskii Duality: An Overview,operty, and the existence of suitable exhaustion functions called Khas’minskii potentials. Applications, also involving the geometry of submanifolds, will be discussed in the last sections. We conclude by investigating the stability of these maximum principles when we remove polar sets.

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Harnack and Pointwise Estimates for Degenerate or Singular Parabolic Equations,re recent developments of the theory for nonlinear degenerate/singular equations, highlighting the differences with the quadratic case and introducing the so-called . Harnack inequalities. Finally, we provide complete proofs of the Harnack inequalities in some paramount case to introduce the reader to the . method.

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Comparison Among Several Planar Fisher-KPP Road-Field Systems,et al. (SIAM J. Math. Anal. 49, 4595–4624, 2017) for two lines bounding a strip. The main goal is to compare the speed of propagation in the direction of the line(s) of these situations with the cases of a plane with one and two lines on which the diffusion is different with respect to the rest of the planar domain.

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Book 2019eral aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications.?The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, over

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Dina Neiger,Leonid Churilov,Andrew Flitmanwhere the classification of certain entire bounded solutions to the fractional Allen-Cahn equation has been obtained. Moreover we describe the connection between the fractional Allen-Cahn equation and the fractional perimeter functional, and we present also some results in the classifications of nonlocal minimal surfaces.

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