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A Local Uniqueness Result for a Quasi-linear Heat Transmission Problem in a Periodic Two-phase Dilute Composite
We consider a quasi-linear heat transmission problem for a composite material which fills the n-dimensional Euclidean space. The composite has a...
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Analytic Dependence of Volume Potentials Corresponding to Parametric Families of Fundamental Solutions
We show that volume potentials associated to a parameter dependent analytic family of weakly singular kernels depend real-analytically upon the...
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More on the Potential for the Farthest-Point Distance Function
For some particular cases in dimension 3 and higher we prove a conjecture of Laugesen and Pritsker (Canad. Math. Bull., 46 , pp. 373–387,
2003 )... -
Growth and approximation of solutions to a class of certain linear partial differential equations in ℝ N
In this paper we consider the equation ∇ 2 φ + A ( r 2 ) X · ∇φ + C ( r 2 ) φ = 0 for X ∈ ℝ N whose coefficients are entire functions of the variable r = | X |....
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Higher-Order Multilinear Poincaré and Sobolev Inequalities in Carnot Groups
The notions of higher-order weighted multilinear Poincaré and Sobolev inequalities in Carnot groups are introduced. As an application, weighted...
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Solution of fractional partial differential equations using iterative method
The purpose of this paper is to obtain solutions for both linear and nonlinear initial value problems (IVPs) for fractional transport equations and...
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Orlicz norm inequalities for the composite operator and applications
In this article, we first prove Orlicz norm inequalities for the composition of the homotopy operator and the projection operator acting on solutions...
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A fascinating polynomial sequence arising from an electrostatics problem on the sphere
A positive unit point charge approaching from infinity a perfectly spherical isolated conductor carrying a total charge of +1 will eventually cause a...
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Integral Representations for Harmonic Functions of Infinite Order in a Cone
A harmonic function of infinite order defined in an n -dimensional cone and continuous in the closure can be represented in terms of the modified...
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On Generalized Integral Means and Euler Type Vector Fields
Formulas for the Euler vector fields, the Neumann derivatives, and the Euler as well as Dirichlet product are derived. Extensions to a Riemann domain...
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Map** Properties of Layer Potentials Associated with Higher-Order Elliptic Operators in Lipschitz Domains
The method of layer potentials has been applied with tremendous success in the treatment of boundary value problems for second-order differential...
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BMO and Lipschitz Norm Estimates for Composite Operators
In this paper, we obtain Lipschitz and BMO norm inequalities for the composition G ∘ T of the homotopy operator T and Green’s operator G applied to...
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On the Compactness of the Hypercomplex Commutator in Hölder Continuous Functions Spaces
This paper is devoted to the compactness of the hypercomplex commutator S γ M a − M a S γ , where S γ is the Cauchy singular integral operator (in the...
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On the Well-posedness of the Dirichlet Problem in Certain Classes of Nontangentially Accessible Domains
We prove that if Ω ⊂ ℝ n is a bounded NTA domain (in the sense of Jerison and Kenig) with an Ahlfors regular boundary,...
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The Integral Equation Method and the Neumann Problem for the Poisson Equation on NTA Domains
The Neumann problem for the Poisson equation is studied on a general open subset G of the Euclidean space. The right-hand side is a distribution F ...
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Riesz and Poisson-Jensen Representation Formulas for a Class of Ultraparabolic Operators on Lie Groups
The aim of this paper is to give some representation formulas of Riesz and Poisson-Jensen type for super-solutions to a class of hypoelliptic...