共查询到20条相似文献,搜索用时 15 毫秒
1.
We establish a number of results on the integrability of the entropy and the weak solutions of the Dirichlet problem for nonlinear elliptic equations of second order depending on the integrability properties of the right-hand sides of these equations. 相似文献
2.
Mathematical Notes - 相似文献
3.
Sensitivity analysis provides useful information for equation-solving, optimization, and post-optimality analysis. However, obtaining useful sensitivity information for systems with nonsmooth dynamic systems embedded is a challenging task. In this article, for any locally Lipschitz continuous mapping between finite-dimensional Euclidean spaces, Nesterov’s lexicographic derivatives are shown to be elements of the plenary hull of the (Clarke) generalized Jacobian whenever they exist. It is argued that in applications, and in several established results in nonsmooth analysis, elements of the plenary hull of the generalized Jacobian of a locally Lipschitz continuous function are no less useful than elements of the generalized Jacobian itself. Directional derivatives and lexicographic derivatives of solutions of parametric ordinary differential equation (ODE) systems are expressed as the unique solutions of corresponding ODE systems, under Carathéodory-style assumptions. Hence, the scope of numerical methods for nonsmooth equation-solving and local optimization is extended to systems with nonsmooth parametric ODEs embedded. 相似文献
4.
5.
6.
We prove the existence of non-smooth solutions to fully non-linear elliptic equations.
Received: June 2006, Accepted: January 2007 相似文献
7.
《Journal of Differential Equations》1996,127(2):439-453
GivenΩany open and bounded subset of n,n⩾4, with smooth boundary and givenΣany (n−m)-dimensional compact submanifold ofΩwithout boundary,n>m>2, we prove the existence of weak solutions to the problem[formula]which are singular onΣ, whenpis a realp>m/(m−2), close to this value. 相似文献
8.
9.
A. L. Baisón A. Clop R. Giova J. Orobitg A. Passarelli di Napoli 《Potential Analysis》2017,46(3):403-430
We study nonlinear elliptic equations in divergence form When \({\mathcal A}\) has linear growth in D u, and assuming that \(x\mapsto {\mathcal A}(x,\xi )\) enjoys \(B^{\alpha }_{\frac {n}\alpha , q}\) smoothness, local well-posedness is found in \(B^{\alpha }_{p,q}\) for certain values of \(p\in [2,\frac {n}{\alpha })\) and \(q\in [1,\infty ]\). In the particular case \({\mathcal A}(x,\xi )=A(x)\xi \), G = 0 and \(A\in B^{\alpha }_{\frac {n}\alpha ,q}\), \(1\leq q\leq \infty \), we obtain \(Du\in B^{\alpha }_{p,q}\) for each \(p<\frac {n}\alpha \). Our main tool in the proof is a more general result, that holds also if \({\mathcal A}\) has growth s?1 in D u, 2 ≤ s ≤ n, and asserts local well-posedness in L q for each q > s, provided that \(x\mapsto {\mathcal A}(x,\xi )\) satisfies a locally uniform VMO condition.
相似文献
$$\text {div }{\mathcal A}(x,Du)=\text {div } G.$$
10.
11.
We consider systems described by boundary-value problems for elliptic second-order partial differential equations with discontinuous coefficients. These systems arise in the study of steady-state processes of a fluid filtration in multicomponent schistous mediums with nonuniform conditions for a nonideal contact. By observing the state of the systems, we find minimax estimates for functionals of the right-hand sides of these equations. Here we suppose that the right-hand sides of the equations, the boundary conditions, the junction conditions, and the error in the measurements are not known precisely, but we know only the sets to which they belong. We show that finding the minimax estimates is reduced to solving some integro-differential equations. 相似文献
12.
Differential Equations - For autonomous systems of ordinary differential equations with fractional-rational right-hand sides for which the nonnegative orthant is positively invariant, sufficient... 相似文献
13.
Louis Nirenberg 《Milan Journal of Mathematics》2011,79(1):3-12
This lecture presents some results by L. Caffarelli, Y.Y. Li, and the speaker, from [2], [3] and [4]. They concern extensions to singular solutions of various forms of the maximum principle; they consist of some small technical
results. 相似文献
14.
15.
We study the existence of positive solutions of the nonlinear elliptic problem
in D with u=0 on D, where and are two Randon's measures belonging to a Kato subclass and D is an unbounded smouth domain in
d(d3). When g is superlinear at 0 and 0f(t)t for t(0,b), then probabilistic methods and fixed point argument are used to prove the existence of infinitely many bounded continuous solutions of this problem. 相似文献
16.
17.
18.
We provide regularity results at the boundary for continuous viscosity solutions to nonconvex fully nonlinear uniformly elliptic equations and inequalities in Euclidian domains. We show that (i) any solution of two sided inequalities with Pucci extremal operators is C 1, α on the boundary; (ii) the solution of the Dirichlet problem for fully nonlinear uniformly elliptic equations is C 2, α on the boundary; (iii) corresponding asymptotic expansions hold. This is an extension to viscosity solutions of the classical Krylov estimates for smooth solutions. 相似文献
19.
通过结合移动平面法及其角点区域的Hopf引理得到了有界区域上一类完全非线性椭圆型方程组解的对称性和单调性. 相似文献
20.
We prove that there is no nontrivial homogeneous order 2 analytic outside zero solutions of fully nonlinear, uniformly elliptic equations in ?. © 2013 Wiley Periodicals, Inc. 相似文献