共查询到20条相似文献,搜索用时 15 毫秒
1.
Giuseppe Mingione 《Mathematische Annalen》2010,346(3):571-627
We show sharp local a priori estimates and regularity results for possibly degenerate non-linear elliptic problems, with data
not lying in the natural dual space. We provide a precise non-linear potential theoretic analog of classical potential theory
results due to Adams (Duke Math J 42:765–778, 1975) and Adams and Lewis (Studia Math 74:169–182, 1982), concerning Morrey
spaces imbedding/regularity properties. For this we introduce a technique allowing for a “non-local representation” of solutions
via Riesz potentials, in turn yielding optimal local estimates simultaneously in both rearrangement and non-rearrangement
invariant function spaces. In fact we also derive sharp estimates in Lorentz spaces, covering borderline cases which remained
open for some while. 相似文献
2.
Gary M. Lieberman 《Annali di Matematica Pura ed Applicata》1993,164(1):103-120
Summary Gradient bounds are proved for solutions to a class of second order elliptic systems in divergence form. The main condition on this class is a generalization of the assumption that the system be the Euler-Lagrange system of equations for a functional depending only on the modulus of the gradient of the solution. 相似文献
3.
《Mathematical Methods in the Applied Sciences》2018,41(1):261-269
In this paper, we study the homogeneous Dirichlet problem for an elliptic equation whose simplest model is where , N≥3 is an open bounded set, θ∈]0,1[, and f belongs to a suitable Morrey space. We will show that the Morrey property of the datum is transmitted to the gradient of a solution. 相似文献
4.
We obtain the global W
1,p
, 1 < p < ∞, estimate for the weak solution of an elliptic system with discontinuous coefficients in non-smooth domains without
using maximal function approach. It is assumed that the boundary of a bounded domain is well approximated by hyperplanes at
every point and at every scale, and that the tensor coefficients belong to BMO space with their BMO semi-norms sufficiently
small.
S.-S. Byun was supported in part by KRF-2006-C00034 and L. Wang was supported in part by NSF Grant 0701392. 相似文献
5.
We study a class of non-homogeneous quasilinear elliptic equations with measure data to obtain an optimal regularity estimate. We prove that the gradient of a weak solution to the problem is as integrable as the first order maximal function of the associated measure in the Orlicz spaces up to a correct power. 相似文献
6.
Yanqin Fang 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2767-2778
In this paper we consider systems of p-q-Laplacian elliptic equations with critical Sobolev exponent. The existence and multiplicity results of solutions are obtained by a limit index method. 相似文献
7.
Dengfeng Lü 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6371-6382
In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic systems with Sobolev critical exponent in a bounded domain. By using the variational method and the Nehari manifold, we obtain the existence and multiplicity results of nontrivial solutions for the systems. 相似文献
8.
Isoperimetric estimates for the first eigenfunction of a class of linear elliptic problems 总被引:1,自引:0,他引:1
M. F. Betta F. Chiacchio A. Ferone 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(1):37-52
We find some optimal estimates for the first eigenfunction of a class of elliptic equations whose prototype is
with Dirichlet boundary condition, where γ is the normalized Gaussian function in
. To this aim we make use of the Gaussian symmetrization which transforms a domain into an half-space with the same Gaussian
measure. The main tools we use are the properties of the weighted rearrangements and in particular the isoperimetric inequality
with respect to Gaussian measure.
Partially supported by GMAMPA - INDAM, Progetto “Proprietà analitico geometriche di soluzioni di equazioni ellittiche e paraboliche”. 相似文献
9.
M. F. Betta F. Chiacchio A. Ferone 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):37-52
We find some optimal estimates for the first eigenfunction of a class of elliptic equations whose prototype is
- ( guxi )xi = lgu \textin W ì \mathbbRn - {\left( {\gamma u_{{x_{i} }} } \right)}_{{x_{i} }} = \lambda \gamma u\,{\text{in}}\,\Omega \subset \mathbb{R}^{n}
with Dirichlet boundary condition, where γ is the normalized Gaussian function in
\mathbbRn \mathbb{R}^{n}
. To this aim we make use of the Gaussian symmetrization which transforms a domain into an half-space with the same Gaussian
measure. The main tools we use are the properties of the weighted rearrangements and in particular the isoperimetric inequality
with respect to Gaussian measure. 相似文献
10.
We consider an elliptic system in divergence form with measurable coefficients in a nonsmooth bounded domain to find a minimal regularity requirement on the coefficients and a lower level of geometric assumption on the boundary of the domain for a global W 1,p , 1 < p < ∞, regularity. It is proved that such a W 1,p regularity is still available under the assumption that the coefficients are merely measurable in one variable and have small BMO semi-norms in the other variables while the domain can be locally approximated by a hyperplane, a so called δ-Reifenberg domain, which is beyond the Lipschitz category. This regularity easily extends to a certain Orlicz-Sobolev space. 相似文献
11.
12.
13.
Guangwen Zhao 《Archiv der Mathematik》2020,114(4):457-469
This paper studies gradient estimates for positive solutions of the nonlinear elliptic equation $$\begin{aligned} \Delta _V(u^p)+\lambda u=0,\quad p\ge 1, \end{aligned}$$on a Riemannian manifold (M, g) with k-Bakry–Émery Ricci curvature bounded from below. We consider both the case where M is a compact manifold with or without boundary and the case where M is a complete manifold. 相似文献
14.
15.
N. E. Barabanov 《Siberian Mathematical Journal》1988,29(4):521-530
Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 4, pp. 12–22, July–August, 1988. 相似文献
16.
17.
18.
In this paper we generalize gradient estimates in Lp space to Orlicz space for weak solutions of elliptic equations of p-Laplacian type with small BMO coefficients in δ-Reifenberg flat domains. Our results improve the known results for such equations using a harmonic analysis-free technique. 相似文献
19.
In this paper we generalize classical Lq, q≥p, estimates of the gradient to the Orlicz space for weak solutions of quasilinear elliptic equations of p-Laplacian type. 相似文献
20.
L. H. de Miranda M. Montenegro 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(5):1683-1699
In this paper we investigate the regularity of solutions for the following degenerate partial differential equation $$\left \{\begin{array}{ll} -\Delta_p u + u = f \qquad {\rm in} \,\Omega,\\ \frac{\partial u}{\partial \nu} = 0 \qquad \qquad \,\,\,\,\,\,\,\,\,\, {\rm on} \,\partial \Omega, \end{array}\right.$$ when ${f \in L^q(\Omega), p > 2}$ and q ≥ 2. If u is a weak solution in ${W^{1, p}(\Omega)}$ , we obtain estimates for u in the Nikolskii space ${\mathcal{N}^{1+2/r,r}(\Omega)}$ , where r = q(p ? 2) + 2, in terms of the L q norm of f. In particular, due to imbedding theorems of Nikolskii spaces into Sobolev spaces, we conclude that ${\|u\|^r_{W^{1 + 2/r - \epsilon, r}(\Omega)} \leq C(\|f\|_{L^q(\Omega)}^q + \| f\|^{r}_{L^q(\Omega)} + \|f\|^{2r/p}_{L^q(\Omega)})}$ for every ${\epsilon > 0}$ sufficiently small. Moreover, we prove that the resolvent operator is continuous and compact in ${W^{1,r}(\Omega)}$ . 相似文献