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Estimates for Green Function and the Poisson Kernels of higher order Dirichlet boundary value problems
 J. Differential Equations
"... Pointwise estimates are derived for the kernels associated to the polyharmonic Dirichlet problem on bounded smooth domains. As a consequence one obtains optimal weighted L pL qregularity estimates for weights involving the distance function. ..."
Abstract

Cited by 16 (2 self)
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Pointwise estimates are derived for the kernels associated to the polyharmonic Dirichlet problem on bounded smooth domains. As a consequence one obtains optimal weighted L pL qregularity estimates for weights involving the distance function.
On `anti'Eigenvalues for Elliptic Systems and a Question of McKenna and Walter
, 2002
"... Introduction McKenna and Walter remarked in [13] that the following linear problem needs more study: v + b v = f in #, v = #v = 0 on ##, (1.1) where # is a bounded domain in R and f a given positive function, say f (#) with p > n. Let us quote (using our notation): ... we should be able to estimate ..."
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Cited by 6 (2 self)
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Introduction McKenna and Walter remarked in [13] that the following linear problem needs more study: v + b v = f in #, v = #v = 0 on ##, (1.1) where # is a bounded domain in R and f a given positive function, say f (#) with p > n. Let us quote (using our notation): ... we should be able to estimate the value b c (#) with the property that for 0 b 0 is noncooperative such that indeed, see [14], the standard maximum principle cannot be used. Nevertheless, by the results in [14] one is able to estimate the value b c (#) from below by using th
Regularity of the solutions for nonlinear biharmonic
, 2007
"... The purpose of this paper is to establish the regularity the weak solutions for the nonlinear biharmonic equation ∆ 2 u + a(x)u = g(x,u), u ∈ H 2 (R N), where the condition u ∈ H 2 (R N) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is ..."
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The purpose of this paper is to establish the regularity the weak solutions for the nonlinear biharmonic equation ∆ 2 u + a(x)u = g(x,u), u ∈ H 2 (R N), where the condition u ∈ H 2 (R N) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense. Key words and phrases: Nonlinear biharmonic equation, regularity, fundamental solutions. AMS: 35B40, 35B65, 35G20, 35J60, 35J30 1
ON THE ITERATED GREEN FUNCTIONS ON A BOUNDED DOMAIN AND THEIR RELATED KATO CLASS OF POTENTIALS HABIB MÂAGLI AND NOUREDDINE ZEDDINI
"... ABSTRACT. We use the results of Zhang [15, 16] and Davies [7] on the behavior of the heat kernel p(t, x, y) on a bounded C 1,1 domain D to find again the result of GrunauSweers [9] concerning the estimates of the iterated Greens functions Gm,n(D). Next, we use these estimates to characterize, by me ..."
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ABSTRACT. We use the results of Zhang [15, 16] and Davies [7] on the behavior of the heat kernel p(t, x, y) on a bounded C 1,1 domain D to find again the result of GrunauSweers [9] concerning the estimates of the iterated Greens functions Gm,n(D). Next, we use these estimates to characterize, by means of p(t, x, y), the Kato class Km,n(D) and we give new examples of functions belonging to this class. Key words and phrases: Green function, Gauss semigroup, Kato class. 2000 Mathematics Subject Classification. 34B27.
Contemporary Mathematics On Domains for Which the Clamped Plate System is Positivity Preserving
"... Abstract. Boggio proved in 1905 that the clamped plate equation is positivity preserving for a disk. It is known that on many other domains such a property fails. In this paper we will show that an affirmative result holds on still a large class of domains. We also survey the available methods in ob ..."
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Abstract. Boggio proved in 1905 that the clamped plate equation is positivity preserving for a disk. It is known that on many other domains such a property fails. In this paper we will show that an affirmative result holds on still a large class of domains. We also survey the available methods in obtaining domains with such property. 1.