共查询到20条相似文献,搜索用时 15 毫秒
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We establish the local Hölder continuity for the nonnegative weak solutions of certain doubly nonlinear parabolic equations possessing a singularity in the time derivative part and a degeneracy in the principal part. The proof involves the method of intrinsic scaling and the setting is a measure space equipped with a doubling non-trivial Borel measure supporting a Poincaré inequality. 相似文献
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M. F. Cherepova 《Differential Equations》2014,50(6):824-834
We consider initial-boundary value problems for a uniformly parabolic equation of arbitrary order 2m in a noncylindrical domain whose lateral boundary is nonsmooth with respect to t. We assume that the lower-order coefficients and the right-hand side of the equation, generally speaking, grow to infinity no more rapidly than some power function when approaching the parabolic boundary of the domain, all coefficients of the equation are locally Hölder, and their Hölder constants can grow near that boundary. We construct a smoothness scale of solutions of such problems in weighted Hölder classes of functions whose higher derivatives may grow when approaching the parabolic boundary of the domain. 相似文献
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This paper proves Hölder continuity of viscosity solutions to certain nonlocal parabolic equations that involve a generalized fractional time derivative of Marchaud or Caputo type. As a necessary and preliminary result, this paper first proves Hölder continuity for viscosity solutions to certain nonlinear ordinary differential equations involving the generalized fractional time derivative. 相似文献
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Xinfu Chen 《应用数学学报(英文版)》1987,3(1):70-96
Consider the degenerate parabolic equations of the type $$u_t = div A(x,t,u,Du) + b(x,t,u,Du)$$ which is of the same nature as $$u_t = div|Du|^p Du + |Du|^{p + 2} (p > 2).$$ This paper is to study the \(C^{1 + \alpha } ,\frac{{1 + \alpha }}{2}\) Hölder continuity of a class of degenerate parabolic equations and the existence and uniqueness of the initial boundary value problem. 相似文献
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Galina Irzhanovna Bizhanova 《Journal of Mathematical Sciences》2010,171(1):9-21
The first and second one-dimensional boundary-value problems for parabolic equations are investigated in the case where the conjugation conditions for all required orders are not satisfied. The existence and uniqueness are proved. Estimates of solutions in classical and weighted Hölder spaces are obtained. We prove that the violation of conjugation for the given functions on the boundary of the domain at the initial-time moment causes the appearance of singular solutions. The order of singularity (as a power of t) is found for the singular solutions for t = 0. 相似文献
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A. V. Ivanov 《Journal of Mathematical Sciences》1991,56(2):2320-2347
For positive bounded generalized solutions of degenerate parabolic equations of the form t 0, m 2, one establishes local Hölder estimates, independent of the lower bounds of the indicated solutions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 171, pp. 70–105, 1989. 相似文献
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We give a proof for the Hölder continuity of functions in the parabolic De Giorgi classes in metric measure spaces. We assume the measure to be doubling, to support a weak (1, p)-Poincaré inequality and to satisfy the annular decay property. 相似文献
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N. L. Gol’dman 《Differential Equations》2012,48(12):1563-1571
We justify statements in Hölder classes of ill-posed inverse problems with terminal observation for parabolic equations with unknown coefficients multiplying the time derivative. On the basis of the duality principle, we prove sufficient conditions for the uniqueness of solutions in these classes. We present examples in which the uniqueness property is lost if the set of admissible solutions is extended and examples of instability of the solutions with respect to errors in the input data. We justify the quasisolution method for constructing approximate solutions stable in these Hölder classes. 相似文献
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G. I. Bizhanova 《Journal of Mathematical Sciences》2005,127(2):1828-1848
We prove local (in time) unique solvability of nonlinear H. Amanns problem in Hölder spaces of functions. Estimates of solutions are obtained in these spaces. Bibliography: 10 titles.Dedicated to Academician O. A. Ladyzhenskaya on the occasion of her jubilee__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 295, 2003, pp. 18–56. 相似文献
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M. F. Cherepova 《Differential Equations》2013,49(1):79-87
We consider the first boundary value problem and the oblique derivative problem for a linear second-order parabolic equation in noncylindrical not necessarily bounded domains with nonsmooth (with respect to t) and noncompact lateral boundary under the assumption that the right-hand side and the lower-order coefficients of the equation may have certain growth when approaching the parabolic boundary of the domain and all coefficients are locally Hölder with given characteristics of the Hölder property. We construct a smoothness scale of solutions of these boundary value problems in Hölder spaces of functions that admit growth of higher derivatives near the parabolic boundary of the domain. 相似文献
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Yongzhong Wang 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(7-8):3289-3302
In this paper, we consider nonnegative weak solutions for a class of degenerate parabolic equations. Using Moser’s method, we get the local boundedness of solutions to equations of this class. Then we prove that the solutions are locally Hölder continuous. 相似文献
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In this paper, we prove the Hölder continuity of solutions of parabolic equations containing the p(x, t)-Laplacian. The degree p must satisfy the so-called logarithmic condition. 相似文献
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Matías G. Delgadino Scott Smith 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(3):577-604
This work focuses on drift-diffusion equations with fractional dissipation in the regime . Our main result is an a priori Hölder estimate on smooth solutions to the Cauchy problem, starting from initial data with finite energy. We prove that for some , the norm of the solution depends only on the size of the drift in critical spaces of the form with and , along with the norm of the initial datum. The proof uses the Caffarelli/Vasseur variant of De Giorgi's method for non-local equations. 相似文献
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We study optimal Hölder type inequalities for the Lorentz spaces L p,s (R, μ), in the range 1 < p < ∞, 1 ≤ s ≤ ∞, for both the maximal and the dual norms. These estimates also give sharp results for the corresponding associate norms. 相似文献
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Using the Borwein–Preiss variational principle and in terms of the proximal coderivative, we provide a new type of sufficient conditions for the Hölder metric subregularity and Hölder error bounds in a class of smooth Banach spaces. As an application, new characterizations for the tilt stability of Hölder minimizers are established. 相似文献
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Positivity - This paper deals with the Hölder metric subregularity property of a certain constraint system in Asplund space. Using the techniques of variational analysis, its main part is... 相似文献