Search results for "Mathematica"

\( L^{1} \) existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions

2007

Abstract In this paper we study the questions of existence and uniqueness of weak and entropy solutions for equations of type − div a ( x , D u ) + γ ( u ) ∋ ϕ , posed in an open bounded subset Ω of R N , with nonlinear boundary conditions of the form a ( x , D u ) ⋅ η + β ( u ) ∋ ψ . The nonlinear elliptic operator div a ( x , D u ) is modeled on the p-Laplacian operator Δ p ( u ) = div ( | D u | p − 2 D u ) , with p > 1 , γ and β are maximal monotone graphs in R 2 such that 0 ∈ γ ( 0 ) and 0 ∈ β ( 0 ) , and the data ϕ ∈ L 1 ( Ω ) and ψ ∈ L 1 ( ∂ Ω ) .

Banach spaces which are r-uniformly noncreasy

2003

Abstract We consider a family of spaces wider than UNC spaces introduced by Prus, and we give some fixed point results in the setting of these spaces.

Coderivatives of multivalued mappings, locally compact cones and metric regularity

1999

On the Minimal Solution of the Problem of Primitives

2000

Abstract We characterize the primitives of the minimal extension of the Lebesgue integral which also integrates the derivatives of differentiable functions (called the C -integral). Then we prove that each BV function is a multiplier for the C -integral and that the product of a derivative and a BV function is a derivative modulo a Lebesgue integrable function having arbitrarily small L 1 -norm.

Multiplication of distributions in any dimension: Applications to δ-function and its derivatives

2009

In two previous papers the author introduced a multiplication of distributions in one dimension and he proved that two one-dimensional Dirac delta functions and their derivatives can be multiplied, at least under certain conditions. Here, mainly motivated by some engineering applications in the analysis of the structures, we propose a different definition of multiplication of distributions which can be easily extended to any spatial dimension. In particular we prove that with this new definition delta functions and their derivatives can still be multiplied.

Asymptotic Behaviors of Solutions to quasilinear elliptic Equations with critical Sobolev growth and Hardy potential

2015

Abstract Optimal estimates on the asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations − Δ p u − μ | x | p | u | p − 2 u = Q ( x ) | u | N p N − p − 2 u , x ∈ R N , where 1 p N , 0 ≤ μ ( ( N − p ) / p ) p and Q ∈ L ∞ ( R N ) .

Multiplicity theorems for the Dirichlet problem involving the p-Laplacian

2003

Multiplicity theorems for the Dirichlet problem involving the p-Laplacian were proved using variational approach. It was shown that there existed an open interval and a positive real number, and each problem admits at least three weak solutions. Results on the existence of at least three weak solutions for the Dirichlet problems were established.

Uniqueness of positive solutions to some nonlinear Neumann problems

2017

Abstract Using the moving plane method, we obtain a Liouville type theorem for nonnegative solutions of the Neumann problem { div ( y a ∇ u ( x , y ) ) = 0 , x ∈ R n , y > 0 , lim y → 0 + ⁡ y a u y ( x , y ) = − f ( u ( x , 0 ) ) , x ∈ R n , under general nonlinearity assumptions on the function f : R → R for any constant a ∈ ( − 1 , 1 ) .

On lifting the approximation property from a Banach space to its dual

2014

Intrinsic characterizations of perturbation classes on some Banach spaces

2010

We investigate relationships between inessential operators and improjective operators acting between Banach spaces X and Y, emphasizing the case in which one of the spaces is a C(K) space. We show that they coincide in many cases, but they are different in the case X=Y =C(K 0), where K 0 is a compact space constructed by Koszmider. Mathematics Subject Classification (2000)47A53 KeywordsInessential operators-Improjective operators-Fredholm theory