Page 1 Alessandro Carbotti, Serena Dipierro, and Enrico Valdinoci Local Density of Solutions
to Fractional Equations Page 2 De Gruyter Studies in Mathematics | Edited by Carsten …

We consider the N-Laplacian Schrödinger equation strongly coupled with higher order
fractional Poisson's equations. When the order of the Riesz potential α is equal to the …

The fractional Laplacian (− Δ) a (-Δ)^a, a∈(0, 1) a∈(0,1), and its generalizations to variable‐
coefficient 2 a 2a‐order pseudodifferential operators PP, are studied in L q L_q‐Sobolev …

This is a survey on the use of Fourier transformation methods in the treatment of boundary
problems for the fractional Laplacian $(-\Delta)^ a $(0< a< 1), and pseudodifferential …

Mean value formulas are of great importance in the theory of partial differential equations:
many very useful results are drawn, for instance, from the well-known equivalence between …

This paper extends the work of Fasshauer and Ye [Reproducing kernels of Sobolev spaces
via a Green kernel approach with differential operators and boundary operators, Adv …

Neumann conditions for the higher order s-fractional Laplacian (−Δ)su with s>1 - ScienceDirect
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We give the explicit formulas for the Green function and the Martin kernel for all integer and
fractional powers of the Laplacian s> 1 in balls. As consequences, we deduce interior and …

We summarize some of the most recent results regarding the theory of higher-order
fractional Laplacians, ie, the operators obtained by considering (non-integer) powers greater …

We study the existence and positivity of solutions to problems involving higher-order
fractional Laplacians $(-\Delta)^ s $ for any $ s> 1$. In particular, using a suitable variational …