scholarly journals On some properties of weak solutions to elliptic equations with divergence-free drifts

Author(s):  
Nikolay Filonov ◽  
Timofey Shilkin
2020 ◽  
Vol 10 (1) ◽  
pp. 895-921
Author(s):  
Daniele Cassani ◽  
Luca Vilasi ◽  
Youjun Wang

Abstract In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter vanishes (which turns the problem into a purely nonlocal one) or goes to infinity (reducing the problem to the classical semilinear Laplace equation) is also investigated.


2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
M. Khiddi

In this paper, we study the existence of infinitely many weak solutions for nonlocal elliptic equations with critical exponent driven by the fractional p-Laplacian of order s. We show the above result when λ>0 is small enough. We achieve our goal by making use of variational methods, more specifically, the Nehari Manifold and Lusternik-Schnirelmann theory.


2016 ◽  
Vol 5 (4) ◽  
Author(s):  
Luisa Consiglieri

AbstractThere are two main objectives in this paper. One is to find sufficient conditions to ensure the existence of weak solutions for some bidimensional thermoelectric problems. At the steady-state, these problems consist of a coupled system of elliptic equations of the divergence form, commonly accomplished with nonlinear radiation-type conditions on at least a nonempty part of the boundary of a


2020 ◽  
Vol 61 (1) ◽  
pp. 011505 ◽  
Author(s):  
Jun Ik Lee ◽  
Jae-Myoung Kim ◽  
Yun-Ho Kim ◽  
Jongrak Lee

1975 ◽  
Vol 104 (1) ◽  
pp. 209-238 ◽  
Author(s):  
C. V. Coffman ◽  
R. J. Duffin ◽  
V. J. Mizel

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