Search results for " Regular"
showing 10 items of 197 documents
Gradient and Lipschitz Estimates for Tug-of-War Type Games
2021
We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p$-harmonic function. Moreover, we establish an improved Lipschitz estimate when boundary values are close to a plane. Such estimates are known to play a key role in the higher regularity theory of partial differential equations. The proofs are based on cancellation and coupling methods as well as an improved version of the cylinder walk argument. peerReviewed
On the second-order regularity of solutions to the parabolic p-Laplace equation
2022
AbstractIn this paper, we study the second-order Sobolev regularity of solutions to the parabolic p-Laplace equation. For any p-parabolic function u, we show that $$D(\left| Du\right| ^{\frac{p-2+s}{2}}Du)$$ D ( D u p - 2 + s 2 D u ) exists as a function and belongs to $$L^{2}_{\text {loc}}$$ L loc 2 with $$s>-1$$ s > - 1 and $$1<p<\infty $$ 1 < p < ∞ . The range of s is sharp.
Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth
2018
We consider a nonlinear elliptic problem driven by the Dirichlet $p$-Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term $f(z, \cdot,y)$. Using topological tools and the asymptotic analysis of a family of perturbed problems, we prove the existence of a positive smooth solution.
The Relocation of the Canons Regular Monastery in Żagań as an Element in the Reform of Interior Life
2019
Lokalizacja, w której znajdowała się instytucja kościelna, odgrywała istotna rolę w życiu wspólnot religijnych średniowiecza. Interakcje z otoczeniem i wzajemne wpływanie na siebie klasztoru i otoczenia mogły wspierać lub hamować rozwój opactwa. Zdarzały się sytuacje, że dochodziło do zmiany miejsca sprawowania służby przez zakonników. Na terenie Śląska mamy nawet dwa przykłady dla konwentów kanoników regularnych. Zarówno klasztor Najświętszej Maryi Panny we Wrocławiu, jak i konwent żagański swoje pierwotne lokalizacje miały w innych miejscach. Przeniesienie klasztoru z Nowogrodu Bobrzańskiego do Żagania w 1284 roku było wydarzeniem, które otwierało dla opactwa nowe szanse i perspektywy, a …
Przykłady łamania reguły zakonnej przez kanoników regularnych z Żagania w średniowieczu w świetle kroniki klasztornej: Jak to, co złe, miało wskazywa…
2020
Życie wewnętrzne w średniowiecznych klasztorach nie zawsze przebiegało w zgodzie z przyjętymi zasadami, które z założenia powinny być przecież rygorystycznie przestrzegane. Dotyczyło to zarówno braci, ojców, wyższych funkcyjnych klasztornych, a nawet samych opatów. Kronika klasztoru kanoników regularnych w Żaganiu dostarcza nam wielu przykładów łamania reguły zakonnej. Nadużywanie alkoholu, zbyt częste kontakty z kobietami czy nieposłuszeństwo wobec przełożonych – to tylko niektóre z problemów, z którymi borykali się żagańscy kanonicy. Wydaje się, że w takim zabytku dziejopisarstwa średniowiecznego pokazywane powinny być raczej pozytywne przykłady, które miały zachęcać do cnotliwego postępo…
The Relocation of the Canons Regular Monastery in Żagań as an Element in the Reform of Interior Life
2019
The location in which a church was based played an important role in the life of religious communities in the Middle Ages. Interactions with society and the mutual influence of a monastery on the surrounding societies could support or inhibit the development of an abbey. There were situations when monks were moved to serve in different locations. In Silesia, we have two examples of canons regular monasteries. Both the monastery of the Blessed Virgin Mary in Wrocław and the convent of Żagań were originally located in other places. As described in the monastery chronicle, the transfer of the monastery from Nowogród Bobrzański to Żagań in 1284 was an event that opened new opportunities and per…
Lebesgue-type decomposition for sesquilinear forms via differences
2022
Definitions of regularity and singularity are proposed for sesquilinear forms with respect to a non-negative one and a correspondent Lebesgue-type decomposition is proved. In contrast to other Lebesgue-type decompositions established in the literature for sesquilinear forms with generic sign, the underlying idea in this paper is to write symmetric forms as the difference of non-negative sesquilinear forms.
Singular (p, q)-equations with superlinear reaction and concave boundary condition
2020
We consider a parametric nonlinear elliptic problem driven by the sum of a p-Laplacian and of a q-Laplacian (a (Formula presented.) -equation) with a singular and (Formula presented.) -superlinear reaction and a Robin boundary condition with (Formula presented.) -sublinear boundary term (Formula presented.). So, the problem has the combined effects of singular, concave and convex terms. We look for positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.
One-loop corrections to light cone wave functions: the dipole picture DIS cross section
2018
We develop methods needed to perform loop calculations in light cone perturbation theory using a helicity basis, refining the method introduced in our earlier work. In particular this includes implementing a consistent way to contract the four-dimensional tensor structures from the helicity vectors with d-dimensional tensors arising from loop integrals, in a way that can be fully automatized. We demonstrate this explicitly by calculating the one-loop correction to the virtual photon to quark-antiquark dipole light cone wave function. This allows us to calculate the deep inelastic scattering cross section in the dipole formalism to next-to-leading order accuracy. Our results, obtained using …
ARGUMENTS FOR THE ESTABLISHMENT OF A SOVEREIGN INVESTMENT FUND IN ROMANIA
2013
The creation of the national development fund was approved in 2006 through the specific legislation. The main argument in supporting the idea of creating this fund was the fact that Romania still had to privatize some more governmental ownership companies and the sums that would be obtained were going to be used according to some very precise rules. Another argument was that the executive power had to assure the financing of some major infrastructure investment projects, to assure the local contribution of the project financed by structural funds and to assure de necessary funds for solving the problems caused by the retrocession of some buildings. The audit report of the Romanian Court of …