共查询到20条相似文献,搜索用时 9 毫秒
1.
G. Makatsaria 《Journal of Mathematical Sciences》2009,160(6):737-744
In the present paper, the structure of solutions of some important classes of singular elliptic systems on the plane are investigated.
In particular, it is proved that the solutions of such systems have in principle nonanalytic behavior in the neighborhood
of fixed singular points. These results make it possible to state correctly the boundary value problems and give their complete
analysis.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 59, Algebra
and Geometry, 2008. 相似文献
2.
Simone Cecchini Rolando Magnanini 《Calculus of Variations and Partial Differential Equations》2010,39(1-2):121-138
We study the minimizer u of a convex functional in the plane which is not Gâteaux-differentiable. Namely, we show that the set of critical points of any C 1-smooth minimizer can not have isolated points. Also, by means of some appropriate approximating scheme and viscosity solutions, we determine an Euler–Lagrange equation that u must satisfy. By applying the same approximating scheme, we can pair u with a function v which may be regarded as the stream function of u in a suitable generalized sense. 相似文献
3.
L. Fejes Tóth 《Acta Mathematica Hungarica》1965,16(3-4):437-440
4.
A. P. Soldatov 《Journal of Mathematical Sciences》2009,160(1):103-115
The space indicated in the title is introduced and studied.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 57, Suzdal
Conference–2006, Part 3, 2008. 相似文献
5.
A vector valued function u(x), solution of a quasilinear elliptic system cannot be too close to a straight line without being regular. 相似文献
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8.
P. I. Kaleda 《Journal of Mathematical Sciences》2011,179(4):475-490
The author studies singular systems, i.e., vector fields with a continuum of singular points, examines the bifurcation of
a slow-fast separatrix loop, and establishes a criterion for the realizability of the slow field. 相似文献
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10.
We show that for any δ∈[0,1) there exists a homogeneous order 2−δ analytic outside zero solution to a uniformly elliptic Hessian equation in R5. 相似文献
11.
We study Hessian fully nonlinear uniformly elliptic equations and show that the second derivatives of viscosity solutions of those equations (in 12 or more dimensions) can blow up in an interior point of the domain. We prove that the optimal interior regularity of such solutions is no more than C1+?, showing the optimality of the known interior regularity result. The same is proven for Isaacs equations. We prove the existence of non-smooth solutions to fully nonlinear Hessian uniformly elliptic equations in 11 dimensions. We study also the possible singularity of solutions of Hessian equations defined in a neighborhood of a point and prove that a homogeneous order 0<α<1 solution of a Hessian uniformly elliptic equation in a punctured ball should be radial. 相似文献
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13.
Teemu Lukkari 《Mathematische Nachrichten》2009,282(12):1770-1787
We prove a removability result for nonlinear elliptic equations withp (x)‐type nonstandard growth and estimate the growth of solutions near a nonremovable isolated singularity. To accomplish this, we employ a Harnack estimate for possibly unbounded solutions and the fact that solutions with nonremovable isolated singularities are p (x)‐superharmonic functions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
In the present paper, we study the existence of solutions to the problem
where is an unbounded domain in with a compact nonempty boundary consisting of finitely many Jordan curves. The goal is to prove an existence theorem for the above problem in a general setting by using Brownian path integration and potential theory.
15.
We prove the existence of a viscosity solution of a fully nonlinear elliptic equation in 24 dimensions with blowing up second derivative. 相似文献
16.
In this paper we establish the existence of at least one smooth positive solution for a singular quasilinear elliptic system involving gradient terms. The approach combines the sub-supersolutions method and Schauder’s fixed point theorem. 相似文献
17.
B. Rowley 《Transactions of the American Mathematical Society》1997,349(8):3149-3179
An index formula is proved for elliptic systems of P.D.E.'s with boundary values in a simply connected region in the plane. Let denote the elliptic operator and the boundary operator. In an earlier paper by the author, the algebraic condition for the Fredholm property, i.e. the Lopatinskii condition, was reformulated as follows. On the boundary, a square matrix function defined on the unit cotangent bundle of was constructed from the principal symbols of the coefficients of the boundary operator and a spectral pair for the family of matrix polynomials associated with the principal symbol of the elliptic operator. The Lopatinskii condition is equivalent to the condition that the function have invertible values. In the present paper, the index of is expressed in terms of the winding number of the determinant of .
18.
In this work we obtain positive singular solutions of where is a sufficiently small perturbation of the cone where has a smooth nonempty boundary and where satisfies suitable conditions. By singular solution we mean the solution is singular at the ‘vertex of the perturbed cone’. We also consider some other perturbations of the equation on the unperturbed cone Ω and here we use a different class of function spaces. 相似文献
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20.
If g is a nondecreasing nonnegative continuous function we prove that any solution of –u+g(u)=0 in a half plane which blows-up locally on the boundary, in a fairly general way, depends only on the normal variable. We extend this result to problems in the complement of a disk. Our main application concerns the exponential nonlinearity g(u)=eau, or power–like growths of g at infinity. Our method is based upon a combination of the Kelvin transform and moving plane method.Mathematics Subject Classification (1991): 35J60Revised version: 30 June 2004 相似文献