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931.
In this paper, we propose an approximation method to study the regularity of solutions to the Isaacs equation. This class of problems plays a paramount role in the regularity theory for fully nonlinear elliptic equations. First, it is a model-problem of a non-convex operator. In addition, the usual mechanisms to access regularity of solutions fall short in addressing these equations. We approximate an Isaacs equation by a Bellman one, and make assumptions on the latter to recover information for the former. Our techniques produce results in Sobolev and Hölder spaces; we also examine a few consequences of our main findings. 相似文献
932.
Let X be a Banach space over F(= R or C) with dimension greater than 2. Let N(X) be the set of all nilpotent operators and B_0(X) the set spanned by N(X). We give a structure result to the additive maps on FI + B_0(X) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on FI + B_0(X) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T) = cAT A~(-1)+ φ(T)I for all T ∈ FI + B_0(X) or Φ(T) = cAT*A~(-1)+ φ(T)I for all T ∈ FI + B_0(X), where c is a nonzero scalar,A is a τ-linear bijective transformation for some automorphism τ of F and φ is an additive functional.In addition, if dim X = ∞, then A is in fact a linear or conjugate linear invertible bounded operator. 相似文献
933.
We prove the strong well-posedness for stochastic differential equations driven by partial α-stable noise and partial Brownian noise. The drift coefficients belong to certain mixed-norm spaces, which generalize the known results even for stochastic differential equations with single noise cases. 相似文献
934.
Daniel Vera 《Mathematische Nachrichten》2019,292(1):195-210
Restricted non linear approximation is a generalization of the N‐term approximation in which a measure on the index set of the approximants controls the type, instead of the number, of elements in the approximation. Thresholding is a well‐known type of non linear approximation. We relate a generalized upper and lower Temlyakov property with the decreasing rate of the thresholding approximation. This relation is in the form of a characterization through some general discrete Lorentz spaces. Thus, not only we recover some results in the literature but find new ones. As an application of these results, we compress and reduce noise of some images with wavelets and shearlets and show, at least empirically, that the L2‐norm is not necessarily the best norm to measure the approximation error. 相似文献
935.
In this paper, we present some alternative definitions of Besov spaces of generalized smoothness, defined via Littlewood–Paley‐type decomposition, involving weak derivatives, polynomials, convolutions and generalized interpolation spaces. 相似文献
936.
In this paper, based on the smooth point of the unit ball and its support linear functional,we show two equivalent formulations of the isometric extension problem between the unit spheres of strictly convex two-dimensional normed spaces. We prove that these equivalent formulations have a positive answer in a special case. 相似文献
937.
Youpei Zhang Limin Zhang Lixi Wen 《Journal of Mathematical Analysis and Applications》2021,493(2):124535
We are concerned with qualitative analysis of weak solutions for a class of magnetic Laplace equations with lack of compactness. By variational arguments, we establish related nonexistence, existence and multiplicity results. 相似文献
938.
Micha Rzeczkowski 《Mathematische Nachrichten》2021,294(1):118-131
In the paper we prove that the Nevanlinna counting function and the Carleson function of analytic self‐maps of finitely connected domains with smooth boundary are equivalent. Using this result we obtain the characterization of compact composition operators on Hardy–Orlicz spaces. 相似文献
939.
Ge DONG 《数学年刊B辑(英文版)》2021,42(3):333-356
In this paper, the author studies the existence of the minimal nonnegative solutions of some elliptic variational inequalities in Orlicz-Sobolev spaces on bounded or unbounded domains. She gets some comparison results between different solutions as tools to pass to the limit in the problems and to show the existence of the minimal solutions of the variational inequalities on bounded domains or unbounded domains. In both cases,coercive and noncoercive operators are handled. The sufficient and necessary conditions for the existence of the minimal nonnegative solution of the noncoercive variational inequality on bounded domains are established. 相似文献
940.
mdat can 《Numerical Methods for Partial Differential Equations》2021,37(1):118-130
In this paper, first, we prove the weighted Hermite–Hadamard–Mercer inequalities for convex functions, after we establish some new weighted inequalities connected with the right‐sides of weighted Hermite–Hadamard–Mercer type inequalities for differentiable functions whose derivatives in absolute value at certain powers are convex. The results presented here would provide extensions of those given in earlier works. 相似文献