scholarly journals Boundedness and a priori estimates of solutions to elliptic systems with Dirichlet-Neumann boundary conditions

2010 ◽  
Vol 9 (3) ◽  
pp. 731-740 ◽  
Author(s):  
Sándor Kelemen ◽  
◽  
Pavol Quittner ◽  
Keyword(s):  
Boundary Conditions ◽  
A Priori Estimates ◽  
A Priori ◽  
Neumann Boundary ◽  
Elliptic Systems ◽  
Neumann Boundary Conditions ◽  
Estimates Of Solutions ◽  
Priori Estimates

scholarly journals A priori estimates for the Fractional p-Laplacian with nonlocal Neumann boundary conditions and applications

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Dimitri Mugnai ◽  
Kanishka Perera ◽  
Edoardo Proietti Lippi
Keyword(s):  
Boundary Conditions ◽  
Morse Theory ◽  
A Priori Estimates ◽  
A Priori ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Priori Estimates ◽  
Variational Tools

<p style='text-indent:20px;'>We first prove that solutions of fractional <i>p</i>-Laplacian problems with nonlocal Neumann boundary conditions are bounded and then we apply such a result to study some resonant problems by means of variational tools and Morse theory.</p>

Existence of bistable waves for a nonlocal and nonmonotone reaction-diffusion equation

2019 ◽  
Vol 150 (2) ◽  
pp. 721-739
Author(s):  
Sergei Trofimchuk ◽  
Vitaly Volpert
Keyword(s):  
Diffusion Equation ◽  
A Priori Estimates ◽  
Travelling Waves ◽  
A Priori ◽  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Nonlocal Nonlinearity ◽  
Estimates Of Solutions ◽  
Priori Estimates

AbstractReaction-diffusion equation with a bistable nonlocal nonlinearity is considered in the case where the reaction term is not quasi-monotone. For this equation, the existence of travelling waves is proved by the Leray-Schauder method based on the topological degree for elliptic operators in unbounded domains and a priori estimates of solutions in properly chosen weighted spaces.

scholarly journals Quasilinear elliptic systems in divergence form associated to general nonlinearities

2018 ◽  
Vol 7 (4) ◽  
pp. 425-447 ◽  
Author(s):  
Lorenzo D’Ambrosio ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Systems ◽  
Divergence Form ◽  
Systems Of Equations ◽  
Quasilinear Elliptic Systems ◽  
Open Set ◽  
Priori Estimates ◽  
Quasilinear Elliptic

AbstractThe paper is concerned with a priori estimates of positive solutions of quasilinear elliptic systems of equations or inequalities in an open set of {\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local assumption near zero. As a consequence, in the case {\Omega=\mathbb{R}^{N}}, we obtain nonexistence theorems of positive solutions. No hypotheses on the solutions at infinity are assumed.

scholarly journals Uniform a priori estimates for elliptic problems with impedance boundary conditions

2020 ◽  
Vol 19 (5) ◽  
pp. 2445-2471
Author(s):  
Théophile Chaumont-Frelet ◽  
◽  
Serge Nicaise ◽  
Jérôme Tomezyk ◽  
Keyword(s):  
Boundary Conditions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Problems ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Priori Estimates

scholarly journals On the Neumann Problem for Monge-Ampére Type Equations

2016 ◽  
Vol 68 (6) ◽  
pp. 1334-1361 ◽  
Author(s):  
Feida Jiang ◽  
Neil S. Trudinger ◽  
Ni Xiang
Keyword(s):  
Global Regularity ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Neumann Boundary ◽  
Natural Conditions ◽  
Priori Estimates ◽  
The Neumann Problem ◽  
Monge Ampere ◽  
Oblique Boundary

AbstractIn this paper, we study the global regularity for regular Monge-Ampère type equations associated with semilinear Neumann boundary conditions. By establishing a priori estimates for second order derivatives, the classical solvability of the Neumann boundary value problem is proved under natural conditions. The techniques build upon the delicate and intricate treatment of the standard Monge-Ampère case by Lions, Trudinger, and Urbas in 1986 and the recent barrier constructions and second derivative bounds by Jiang, Trudinger, and Yang for the Dirichlet problem. We also consider more general oblique boundary value problems in the strictly regular case.

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