Holder Estimates Research Articles

L p -Theory of Parabolic SPDEs Degenerating on the Boundary of C 1 Domains

Degenerate stochastic partial differential equations are considered in C1 domains. Existence and uniqueness results are given in weighted Sobolev spaces, and Holder estimates of the solutions are presented.

Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains

We establish the global Holder estimates for solutions to second-order elliptic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded. For nondivergence elliptic equations in domains satisfying an cone condition, similar results were obtained by J. H. Michael, who in turn relied on the barrier techniques due to K. Miller. Our approach is based on special growth lemmas, and it works for both divergence and nondivergence, elliptic and parabolic equations, in domains satisfying a general exterior measure condition.

A dual approach to regularity in thin film micromagnetics

We prove a regularity result in the two-dimensional theory of soft ferromagnetic films. The associated Euler–Lagrange equation is given by a nonlocal degenerate variational inequality involving fractional derivatives. A difference quotient type argument based on a dual formulation in terms of magnetostatic potentials yields a Holder estimate for the uniquely determined gradient projection of the magnetization field.

Uniform Hölder Estimates in a Class of Elliptic Systems and Applications to Singular Limits in Models for Diffusion Flames

The main result of this paper is a general Holder estimate in a class of singularly perturbed elliptic systems. This estimate is applied to the study of the well-known Burke–Schuman approximation in flame theory. After reviewing some classical cases (equidiffusional case; high activation energy approximation) we turn to the non-equidiffusional case, and to nonlinear diffusion models. The limiting problems are nonlinear elliptic equations; they have Holder or Lipschitz maximal global regularity. A natural question is then whether this regularity is kept uniformly throughout the approximation process, and we show that this is true in general.

Improved time series prediction with a new method for selection of model parameters

A new method for model selection in prediction of time series is proposed. Apart from the conventional criterion of minimizing RMS error, the method also minimizes the error on the distribution of singularities, evaluated through the local Holder estimates and its probability density spectrum. Predictions of two simulated and one real time series have been done using kernel principal component regression (KPCR) and model parameters of KPCR have been selected employing the proposed as well as the conventional method. Results obtained demonstrate that the proposed method takes into account the sharp changes in a time series and improves the generalization capability of the KPCR model for better prediction of the unseen test data.

Parabolic SPDEs Degenerating on the Boundary of Non-Smooth Domain

Degenerate stochastic partial differential equations of divergence and non-divergence forms are considered in non-smooth domains. Existence and uniqueness results are given in weighted Sobolev spaces, and Holder estimates of the solutions are presented.

Holder estimates for solutions of integro differential equations like the fractional laplace

We provide a purely analytical proof of Holder continuity for harmonic functions with respect to a class of integro-differential equations like the ones associated with purely jump processes. The assumptions on the operator are more flexible than in previous works. Our assumptions include the case of an operator with variable order, without any continuity assumption in that order.

Partial regularity results for evolutional p -Laplacian systems with natural growth

We study a regularity for evolutional p-Laplacian systems with natural growth on the gradient. It is shown that weak solutions of small image and their gradients are partial Holder continuous and the size of the exceptional set for regularity is estimated in terms of Hausdorff measure. The main ingredient is to improve the Gehring inequality, which implies the higher integrability of the gradient and was first developed by Kinnunen and Lewis, so as to be well-worked in our perturbation estimate. We also use a refinement of the perturbation argument and make a device for Holder estimates of the gradient.

Local Hölder regularity of gradients for evolutional p-Laplacian systems

We study a Holder regularity of gradients for evolutional p-Laplacian systems with Holder continuous coefficients and exterior force. We use the perturbation argument with the p-Laplacian systems with constant coefficients and only principal terms. The main task is to make the Holder estimate of gradients for the systems above well-worked in the perturbation estimate. We also need to make a localization of the Holder estimate in [2].

HöLDER ESTIMATES FOR ∂ IN ANALYTIC POLYHEDRA

We consider Holder estimates for ∂ in analytic polyhedra. In the case of dimension 2, it preserves exact Ho1der regularity, and it maps bounded (0,1)-forms into BMO with respect to volume measure.

Hölder estimates of solutions to difference partial differential equations of elliptic-parabolic type

For solutions to difference partial differential equations of elliptic-parabolic type, there is achieved Holder estimates independent of the time discrete mesh.

Minimal surfaces in a wedge

Continuing our papers [4]–[6] we study the global behaviour of minimal surfaces in a wedge which meet the faces of the wedge perpendicularly and are transversal to the edge. We derive a Holder estimate for the Gauss maps of such surfaces which immediately implies a Bernstein–type result: Each complete minimal sector in the wedge of the type described before is necessarily a plane sector. The method uses in an essential way ideas developed in [2], [3], [5], and [9].

Hölder estimates for a natural class of equations of the type of fast diffusion

Holder estimates for weak solutions of doubly nonlinear parabolic equations of the type of fast diffusion with coefficients satisfying only natural growth conditions and the monotonicity requirement are obtained. Bibliography: 17 titles.

Heat kernels of multiplicative perturbations: Holder estimates and Gaussian lower bounds

Heat kernels of multiplicative perturbations: Holder estimates and Gaussian lower bounds

Hölder estimates for the $$\bar \partial - equation$$ in some domains of finite typein some domains of finite type

We obtain Holder estimates for the\(\bar \partial - equation\) on some domains of finite type in ℂn using proper mapping techniques. The domains considered are domains of finite type in the sense of D’Angelo and are defined by local coordinate expressions satisfying certain algebraic geometric conditions which prevent the existence of complex analytic varieties in the boundary of the domain. Using a proper mapping which is given by the finite type condition and which carries all the information about the intrinsic geometry of the boundary, we transform the finite type points into strongly pseudoconvex ones. At these strongly pseudoconvex points we compute an explicit solution using the Henkin integral formula and we obtain estimates that we are able to pull back to the original domain. We achieve this by exploiting the branching behavior of the proper mapping. We also construct some biholomorphic numerical invariants associated with some of the domains under consideration.

Hölder estimates for equations of slow and normal diffusion type

Holder estimates for weak solutions of a certain class of doubly nonlinear parabolic equations of slow or normal diffusion type are established. Bibliography:9 titles.

Some counterexamples to the regularity of Monge-Ampère equations

We present examples to show that the solution u of the Monge-Ampère equation det ( D 2 u ) = f ( x ) \det ({D^2}u) = f(x) , with u = 0 u = 0 on the boundary, may not lie in W 2 , p {W^{2,p}} or in C 1 , α {C^{1,\alpha }} for noncontinuous and positive f ( x ) f(x) and for continuous and nonnegative f ( x ) f(x) .

Holder Estimates for Local Solutions of Some Doubly Nonlinear Degenerate Parabolic Equations

We prove interior and boundary Holder continuity for bounded weak soluttions of a class of quasilinear parabolic equations whose prototype is ut = div(|u|m − 1 |Du|p − 2Du).

Classical solutions of the nondivergent barotropic equations on the sphere*

The nondivergent barotropic equations on the shape provide the simplest mathematical model for the description of large–scale horizontal motions of the atmosphere. This article is concerned with the global existence, uniqueness, and regularity properties of classical solutions of these equations. The proofs are based on Holder estimates of the solutions. AMS(MOS) Subject Classification. Primary 76C05, 76C15. Secondary 35A05.

Hölder estimates for quasilinear doubly degenerate parabolic equations

For positive bounded generalized solutions of degenerate parabolic equations of the form t≥ 0, m≥ 2, one establishes local Holder estimates, independent of the lower bounds of the indicated solutions.