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对于具有VMO间断系数的散度型拟线性退化椭圆型方程,考虑了低阶项微分项在可控制增长条件下的弱解梯度的Morrey空间Lp,λ局部正则性,从而在已知数据正则性提高的条件下得到弱解具有优化Hlder指数的Hlder连续性结果。 相似文献
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本文证明了带有L1资料和对以散度形式的低阶项没作任何增长假设的某类抛物问题熵解的存在性. 相似文献
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本文提出了低阶项系数具一定奇异性的高阶强椭圆微分算子生成解析半群的条 件,其包含了低阶项系数属于Schecter位势类的情形.特别地,低阶项系数属于LP(Rn) 的情形也在其中.作为应用,得到低阶项系数属于LP(Rn)的强椭圆算子的相应半群生 成,且p还可取到一些临界值. 相似文献
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对于低阶项满足自然增长条件的半线性次椭圆方程有界弱解,通过Moser-Nash迭代和弱Harnack不等式,得到弱解的内部H?lder连续性估计. 相似文献
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自然增长下的具VMO系数拟线性椭圆组的部分正则性 总被引:1,自引:0,他引:1
设散度型拟线性系数算子关于自变量x一致满足VMO的结构条件,对于低阶项满足自然增长条件的拟线性椭圆方程组,建立了其弱解具有确切Holder指数的部分正则性. 相似文献
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利用Brown运动在H\"older 范数下关于$(r,p)$-容度的大偏差,证明了Brown运动增量在H\"older范数下关于$(r,p)$-容度的泛函极限定理. 相似文献
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文中利用散度型非线椭圆性算子的Green函数与Laplacian算子的比较性质, 建立了具有自然增长条件下的散度型非线性椭圆方程弱解的内部H\"older连续性. 相似文献
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利用与分数次积分相关的Olsen型不等式,我们得到了薛定谔型椭圆方程的内部Morrey估计, 其中位势函数满足反H\"older条件. 相似文献
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A mollification method for ill-posed problems 总被引:3,自引:0,他引:3
Summary.
A mollification method for a class of ill-posed
problems is suggested. The idea of the method is very simple and
natural: if the data are given inexactly then we try to find a
sequence of ``mollification operators" which map the improper
data into well-posedness classes of the problem (mollify the
improper data). Within these mollified data our problem becomes
well-posed. And when these facts are in hand we try to obtain
error estimates and optimal or ``quasi-optimal" mollification
parameters. The
method is working not only for problems in Hilbert spaces, but
also for problems in Banach spaces. Applications of the
method to concrete problems, like numerical differentiation,
parabolic equations backwards in time, the Cauchy problem for the
Laplace equation,
one- and multidimensional non-characteristic Cauchy problems for
parabolic equations (in infinite or finite domains),... give us
very sharp stability estimates of H\"older continuous type. In
these cases the method is optimal in the sense that it gives the
same order of H\"older continuous dependence on the data as for
the regularized problems. Furthermore, the method may be
implemented numerically using fast Fourier transforms. For the
first time a uniform stability estimate of H\"older continuous
type of the solution of the heat equation backwards in time in the
space for all could
be established by our mollification method. A new simple sharp
pointwise estimate of H\"older type for the weak solution of a
non-characteristic Cauchy problem for parabolic equations in a
finite domain is established.
Received June 25, 1993 / Revised version received February
18, 1994 相似文献
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当p≥ 2时,得到一类低于临界增长的退化椭圆型方程组弱解微商属于局部Morrey-Campanauo空间$L^{ p,\lambda}$和${\cal L}^{p, \gamma}$;在附加条件下,进一步建立其弱解微商的局部H\"older连续性. 相似文献
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利用大偏差,得到了二参数L\'evy区域在H\"older 范数下的局部Strassen重对数律. 相似文献
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S. A. Nazarov 《Journal of Mathematical Sciences》2001,107(3):3860-3873
The existence of a small solution to the quasilinear Neumann problem is established in a H\"older class with separated asymptotics. The lower-order asymptotic terms are constructed. The homogeneity exponents of these terms turn out to be dependent on the value of the solution at a conical point. Bibliography: 33 titles. 相似文献
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{Well-posedness of degenerate differential equations with infinite delay in Holder continuous function spaces
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Using operator-valued $\dot{C}^\alpha$-Fourier multiplier results on vector- valued H\"older continuous function spaces, we give a characterization for the $C^\alpha$-well-posedness of the first order degenerate differential equations with infinite delay $(Mu)"(t) = Au(t) + \int_{-\infty}^t a(t-s)Au(s)ds + f(t)$ ($t\in\R$), where $A, M$ are closed operators on a Banach space $X$ such that $D(A)\cap D(M)\neq \{0\}$, $a\in L^1_{\rm{loc}}(\R_+)\cap L^1(\mathbb{R}_+; t^\alpha dt)$. 相似文献
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朱晓睿 《数学年刊A辑(中文版)》2011,32(6):745-752
给出了一些紧致~K\"{a}hler~流形上具有和时间相关的位势热方程的正解的Hanack估计.作为应用, 得到了两个~K\"{a}hler-Ricci~流下具有非负双截面曲率的单调熵. 相似文献