scholarly journals Sharp estimates for solutions to elliptic problems with mixed boundary conditions

2020 ◽  
Author(s):  
A. Alvino ◽  
F. Chiacchio ◽  
C. Nitsch ◽  
C. Trombetti
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Elliptic Problems ◽  
Mixed Boundary Conditions ◽  
Sharp Estimates

LINEAR ELLIPTIC PROBLEMS WITH MIXED BOUNDARY CONDITIONS RELATED TO RADIATION HEAT TRANSFER

2002 ◽  
Vol 12 (04) ◽  
pp. 541-565 ◽  
Author(s):  
MARIA MICHAELA PORZIO ◽  
ÓSCAR LÓPEZ-POUSO
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Mixed Boundary ◽  
Radiation Heat Transfer ◽  
Elliptic Problems ◽  
Mixed Boundary Conditions ◽  
Radiation Heat ◽  
Neumann Problems ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We prove the existence and uniqueness results for elliptic problems with L1 data and mixed boundary conditions which include as particular cases the Dirichlet and the Neumann problems. These elliptic equations are related to radiation heat trasfer.

scholarly journals EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO ELLIPTIC PROBLEMS WITH SUBLINEAR MIXED BOUNDARY CONDITIONS

2009 ◽  
Vol 11 (04) ◽  
pp. 585-613 ◽  
Author(s):  
JORGE GARCÍA-MELIÁN ◽  
JULIO D. ROSSI ◽  
JOSÉ C. SABINA DE LIS
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Mixed Boundary ◽  
Elliptic Problems ◽  
Mixed Boundary Conditions ◽  
Nonlinear Boundary Conditions ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Outward Unit

In this work, we consider a class of semilinear elliptic problems with nonlinear boundary conditions of mixed type. Under some monotonicity properties of the nonlinearities involved, we show that positive solutions are unique, and that their existence is characterized by the sign of some associated eigenvalues. One of the most important contributions of this work relies on the fact that we deal with boundary conditions of the form ∂u/∂ν = g(x,u) on Γ and u = 0 on Γ', where ν is the outward unit normal to Γ while Γ,Γ' are open, Γ ∩ Γ' = ∅, [Formula: see text], but [Formula: see text] need not be disjoint.

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