scholarly journals Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data

1996 ◽  
Vol 13 (5) ◽  
pp. 539-551 ◽  
Author(s):  
Lucio Boccardo ◽  
Thierry Gallouët ◽  
Luigi Orsina
Keyword(s):  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Elliptic Equations ◽  
Entropy Solutions ◽  
Measure Data ◽  
Nonlinear Elliptic

scholarly journals Entropy Solutions of Doubly Nonlinear Fractional Laplace Equations

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Niklas Grossekemper ◽  
Petra Wittbold ◽  
Aleksandra Zimmermann
Keyword(s):  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Fractional Laplacian ◽  
Nonlinear Elliptic Equations ◽  
Entropy Solutions ◽  
First Order ◽  
Nonlinear Elliptic ◽  
Laplace Equations ◽  
Whole Space ◽  
Doubly Nonlinear

AbstractIn this contribution, we study a class of doubly nonlinear elliptic equations with bounded, merely integrable right-hand side on the whole space $$\mathbb {R}^N$$ R N . The equation is driven by the fractional Laplacian $$(-\varDelta )^{\frac{s}{2}}$$ ( - Δ ) s 2 for $$s\in (0,1]$$ s ∈ ( 0 , 1 ] and a strongly continuous nonlinear perturbation of first order. It is well known that weak solutions are in genreral not unique in this setting. We are able to prove an $$L^1$$ L 1 -contraction and comparison principle and to show existence and uniqueness of entropy solutions.

Existence results for the Dirichlet problem of some degenerate nonlinear elliptic equations

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic

AbstractIn this paper we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated to the degenerate nonlinear elliptic equations

On some nonlinear elliptic equations involving derivatives of the nonlinearity

1985 ◽  
Vol 100 (3-4) ◽  
pp. 281-294 ◽  
Author(s):  
J. Carrillo ◽  
M. Chipot
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Elliptic Boundary ◽  
Nonlinear Elliptic Equations ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Nonlinear Elliptic ◽  
Image Position ◽  
Derivatives Of

SynopsisWe give some results on existence and uniqueness for the solution of elliptic boundary value problems of typewhen the βi are not necessarily smooth.

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