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We show the existence of a continuous solution to a nonlinear parabolic obstacle problem with a continuous time-dependent obstacle. The solution is constructed by an adaptation of the Schwarz alternating method. Moreover, if the obstacle is Hölder continuous, we prove that the solution inherits the same property. 相似文献
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We state and prove a general Harnack inequality for minimizers of nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian. 相似文献
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We prove that a solution of an elliptic operator with periodic coefficients behaves on large scales like an analytic function in the sense of approximation by polynomials with periodic corrections. Equivalently, the constants in the large-scale Ck, 1 estimate scale exponentially in k , just as for the classical estimate for harmonic functions, and the minimal scale grows at most linearly in k . As a consequence, we characterize entire solutions of periodic, uniformly elliptic equations that exhibit growth like O(exp(δ| x| )) for small δ > 0 . The large-scale analyticity also implies quantitative unique continuation results, namely a three-ball theorem with an optimal error term as well as a proof of the nonexistence of L2 eigenfunctions at the bottom of the spectrum. © 2020 Wiley Periodicals LLC. 相似文献
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Karri Muinonen Tuomo Pieniluoma 《Journal of Quantitative Spectroscopy & Radiative Transfer》2011,112(11):1747-1752
We introduce the stochastic geometry of a Gaussian random ellipsoid (GE) and, with the discrete-dipole approximation, carry out preliminary computations for light scattering by wavelength-scale GE particles. In the GE geometry, we describe the base ellipsoid by the three semiaxes a?b?c. The axial ratios b:a and c:a appear as two shape parameters additional to those of the Gaussian random sphere geometry (GS). We compare the scattering characteristics of GE particles to those of ellipsoids. Introducing irregularities on ellipsoids smoothens the angular scattering characteristics, in a way analogous to the smoothening of spherical particle characteristics in the case of GS particles. 相似文献
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Tuomo Kuusi Rojbin Laleoglu Juhana Siljander José Miguel Urbano 《Calculus of Variations and Partial Differential Equations》2012,45(1-2):193-229
We complete the study of the regularity for Trudinger’s equation by proving that weak solutions are H?lder continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincaré inequality. The proof uses the Harnack inequality and intrinsic scaling. 相似文献
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Janne Martikainen Tuomo Rossi Jari Toivanen 《Numerical Linear Algebra with Applications》2002,9(8):629-652
A fast direct solution method for a discretized vector‐valued elliptic partial differential equation with a divergence constraint is considered. Such problems are typical in many disciplines such as fluid dynamics, elasticity and electromagnetics. The method requires the problem to be posed in a rectangle and boundary conditions to be either periodic boundary conditions or the so‐called slip boundary conditions in one co‐ordinate direction. The arising saddle‐point matrix has a separable form when bilinear finite elements are used in the discretization. Based on a result for so‐called p‐circulant matrices, the saddle‐point matrix can be transformed into a block‐diagonal form by fast Fourier transformations. Thus, the fast direct solver has the same structure as methods for scalar‐valued problems which are based on Fourier analysis and, therefore, it has the same computational cost ??(N log N). Numerical experiments demonstrate the good efficiency and accuracy of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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Tuomo Tikkanen 《Radiation Physics and Chemistry》1997,50(6):527-534
Experimental X-ray absorption cross sections were abstracted from synchrotron radiation transmission measurements of aluminium coated polyimide membranes. Edge structure data are presented in tables for carbon in the range 283.4–400 eV, for nitrogen in 402–529 eV, for oxygen in 529.5–750 eV and for aluminium in 60–283.2 eV and 1554–1800 eV. 相似文献