An approximate analytical solution is obtained for hypersonic flow past a slender elliptic cone using second-order perturbation techniques in spherical coordinate systems. The analysis is based on perturbations of hypersonic flow past a circular cone aligned with the free stream, the perturbations stemming from the small cross-section eccentricity. By means of hypersonic approximations for the ...

Green’s formulas for elliptic cone differential operators are established. This is done by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint, thereby utilizing the concept of a discrete asymptotic type. From this description, the singular coefficients replacing the boundary traces in classical Green’s formulas are deduced. CONTENTS

In this paper we will study under which conditions the positive cone, or part of the positive cone, is preserved when solving a weakly coupled system of elliptic partial differential equations. Such a system will be as follows:  −∆1 0 0 . . . 0 0 −∆k   u1 .. uk  =  c11 · · · c1k .. .. ck1 · · · ckk   u1 .. uk +  f1 .. fk  on a bounded domain in IR, with zero Dirichlet bounda...

This note discusses some aspects of the analysis leading to the proof of the main theorem in [10] (stated here as Theorem 1) on the structure of the asymptotics of the resolvent trace of a general elliptic cone operator as the spectral parameter tends to infinity, under suitable minimal growth assumptions on the principal symbols of the operator. We deal with an elliptic cone differential operator

Abstract. We analyze the behavior of the trace of the resolvent of an elliptic cone differential operator as the spectral parameter tends to infinity. The resolvent splits into two components, one associated with the minimal extension of the operator, and another, of finite rank, depending on the particular choice of domain. We give a full asymptotic expansion of the first component and expand ...

In this paper, we study the motion of level sets by general curvature. The difficulty in this setting is for a general curvature function, it’s only well defined in an admissible cone. In order to extend the existence result to outside the cone we introduce a new approximation function f̂ (see (3.1)). Moreover, using the idea in [5], we give an elliptic approach for the Ben-Andrews’ non-collapsi...

We prove the existence of sectors of minimal growth for general closed extensions of elliptic cone operators under natural ellipticity conditions. This is achieved by the construction of a suitable parametrix and reduction to the boundary. Special attention is devoted to the clarification of the analytic structure of the resolvent.

We study the adjointness problem for the closed extensions of a general b-elliptic operator A ∈ x Diffmb (M ;E), ν > 0, initially defined as an unbounded operator A : C∞ c (M ;E) ⊂ x L b (M ;E) → xL b (M ;E), μ ∈ R. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.