共查询到20条相似文献,搜索用时 15 毫秒
1.
Maria Michaela Porzio Flavia Smarrazzo Alberto Tesei 《Calculus of Variations and Partial Differential Equations》2014,51(1-2):401-437
We prove the existence of suitably defined weak Radon measure-valued solutions of the homogeneous Dirichlet initial-boundary value problem for a class of strongly degenerate quasilinear parabolic equations. We also prove that: \((i)\) the concentrated part of the solution with respect to the Newtonian capacity is constant; \((ii)\) the total variation of the singular part of the solution (with respect to the Lebesgue measure) is nonincreasing in time. Conditions under which Radon measure-valued solutions of problem \((P)\) are in fact function-valued (depending both on the initial data and on the strength of degeneracy) are also given. 相似文献
2.
3.
Weilin Zou 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):3069-3082
This paper deals with a class of degenerate quasilinear elliptic equations of the form −div(a(x,u,∇u)=g−div(f), where a(x,u,∇u) is allowed to be degenerate with the unknown u. We prove existence of bounded solutions under some hypothesis on f and g. Moreover we prove that there exists a renormalized solution in the case where g∈L1(Ω) and f∈(Lp′(Ω))N. 相似文献
4.
5.
6.
For quasilinear equations div A(x, u, ∇u) = 0 with degeneracy ω(x) of the Muckenhoupt A
p
-class, we prove the Harnack inequality, an estimate for the H?lder norm, and a sufficient criterion for the regularity of
boundary points of the Wiener type.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 918–936, July, 2008. 相似文献
7.
Summary We prove the existence of bounded solutions in L () of degenerate elliptic boundary value problems of second order in divergence form with natural growth in the gradient. For the Dirichlet problem our results cover also unbounded domains .Work performed under the auspicies of G.N.A.F.A. of the C.N.R., partially supported by M.P.I. of Italy (40%). 相似文献
8.
We consider the Dirichlet problem for a class of anisotropic degenerate elliptic equations. 相似文献
9.
The current paper is concerned with constructing multibump type solutions for a class of quasilinear Schrödinger type equations including the Modified Nonlinear Schrödinger Equations. Our results extend the existence results on multibump type solutions in Coti Zelati and Rabinowitz (1992) [17] to the quasilinear case. Our work provides a theoretic framework for dealing with quasilinear problems, which lack both smoothness and compactness, by using more refined variational techniques such as gluing techniques, Morse theory, Lyapunov–Schmidt reduction, etc. 相似文献
10.
11.
Peter Lindqvist 《Journal d'Analyse Mathématique》1993,61(1):283-292
We study an integrability phenomenon for elliptic equations in divergence form. We prove that solutions and supersolutions
that are bounded from below are globally integrable to some power. This extends a result known for harmonic functions to a
nonlinear situation. We use BMO techniques. 相似文献
12.
We consider a nonlinear (possibly) degenerate elliptic operator where the field a and the function b are (unnecessarily strictly) monotonic and a satisfies a very mild ellipticity assumption. For a given boundary datum ? we prove the existence of the maximum and the minimum of the solutions and formulate a Haar-Radò type result, namely a continuity property for these solutions that may follow from the continuity of ?. In the homogeneous case we formulate some generalizations of the Bounded Slope Condition and use them to obtain the Lipschitz or local Lipschitz regularity of solutions to Lu=0. We prove the global Hölder regularity of the solutions in the case where ? is Lipschitz. 相似文献
13.
Giovanna Citti 《Annali di Matematica Pura ed Applicata》1991,158(1):315-330
Sunto Viene provato un teorema di esistenza di soluzioni positive per una certa classe di equazioni quasilineari ellittiche degeneri su aperti non limitati di Rn utilizzando un metodo di confronta all'infinito. 相似文献
14.
We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence
form under natural growth conditions. The degeneracy is given by a suitable power of a strong A
∞ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove C
1,α
local estimates for solutions of a degenerate equation in non divergence form. 相似文献
15.
We prove local and global regularity for the positive solutions of a quasilinear variational degenerate equation, assuming minimal hypothesis on the coefficients of the lower order terms. As an application we obtain Hölder continuity for the gradient of solutions to nonvariational quasilinear equations. 相似文献
16.
17.
18.
Entire solutions of quasilinear elliptic equations 总被引:1,自引:0,他引:1
James Serrin 《Journal of Mathematical Analysis and Applications》2009,352(1):3-4436
We study entire solutions of non-homogeneous quasilinear elliptic equations, with Eqs. (1) and (2) below being typical. A particular special case of interest is the following: Let u be an entire distribution solution of the equation Δpu=|u|q−1u, where p>1. If q>p−1 then u≡0. On the other hand, if 0<q<p−1 and u(x)=o(|x|p/(p−q−1)) as |x|→∞, then again u≡0. If q=p−1 then u≡0 for all solutions with at most algebraic growth at infinity. 相似文献
19.