1,720,989 research outputs found
A new short proof of regularity for local weak solutions for a certain class of singular parabolic equations
Full text linkWe shall establish the interior Holder continuity for locally bounded weak solutions to a class of parabolic singular equations whose prorotypes are the p-Laplacean and the doubly-nonlinear equation, via a new and simplified proof using recent techniques on expansion of positivity and L1-Harnack estimates
Harnack-type estimates and extinction in finite time for a class of anisotropic porous medium type equations
Full text linkIn this work we are interested in the study of a class of anisotropic porous medium-type equations, for which we derive several estimates, namely two Harnack-type inequalities; and, when considering the associated Dirichlet problem, we determine the finite time of extinction and thereby present a decay rate of extinction
Fine Boundary Continuity for Degenerate Double-Phase Diffusion
Full text linkWe study the boundary behavior of solutions to parabolic double-phase equations through the celebrated Wiener’s sufficiency criterion. The analysis is conducted for cylindrical domains and the regularity up to the lateral boundary is shown in terms of either its p or q capacity, depending on whether the phase vanishes at the boundary or not. Eventually we obtain a fine boundary estimate that, when considering uniform geometric conditions as density or fatness, leads us to the boundary Hölder continuity of solutions. In particular, the double-phase elicits new questions on the definition of an adapted capacity
On a Particular Scaling for the Prototype Anisotropic p-Laplacian
Full text linkIn this brief note we show that under a volume non-preserving scaling it is possible to recover the basics for a regularity theory regarding local weak solutions to the fully anisotropic equation 1∂tu=∑i=1N∂i(|∂iu|pi−2∂iu)inΩT=Ω×(−T,T),withΩ⊂⊂RN.We characterize self-similar solutions regarding this particular scaling and we show that semi-continuity for solutions to this equation is a consequence of a simple property that is itself invariant under scaling
On the continuity of solutions to anisotropic elliptic operators in the limiting case
Full text linkWe show that local weak solutions to anisotropic elliptic equations with bounded and measurable coefficients are continuous. Our analysis exploits a particular intrinsic geometry that, within the limiting case on the exponents, allows for a reduction of the oscillation of the solution
The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth
No full textIn this work we prove that the non-negative functions belonging to suitable non-homogeneous (non-uniformly elliptic) De Giorgi classes, satisfy a weak Harnack inequality with a constant depending on the Ls-norm of the solution. Under suitable assumptions, the minimizers of elliptic functionals with generalized Orlicz growth belong to De Giorgi classes satisfying the above condition; thus this study gives a wider interpretation of Harnack-type estimates derived to double-phase, degenerate double-phase functionals and functionals with variable exponents
The impact of intrinsic scaling on the rate of extinction for anisotropic non-Newtonian fast diffusion
No full textWe study the decay towards the extinction that pertains to local weak solutions to fully anisotropic equations. Their rates of extinction are evaluated by means of several integral Harnack-type inequalities which constitute the core of our analysis and that are obtained for anisotropic operators having full quasilinear structure. Different decays are obtained when considering different space geometries. The approach is motivated by the research of new methods for strongly nonlinear operators, hence dispensing with comparison principles, while exploiting an intrinsic geometry that affects all the variables of the solution
Liouville rigidity and time-extrinsic Harnack estimates for an anisotropic slow diffusion
Full text linkWe prove that ancient non-negative solutions to a fully anisotropic prototype
evolution equation are constant if they satisfy a condition of finite speed of
propagation and if they are both one-sided bounded, and bounded in space at a
single time level. A similar statement is valid when the bound is given at a
single space point. As a general paradigm, H\"older estimates provide the
basics for rigidity. Finally, we show that recent intrinsic Harnack estimates
can be improved to a Harnack inequality valid for non-intrinsic times. Locally,
they are equivalent.Comment: 15 page
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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