Search results for " solution"
showing 10 items of 3084 documents
Mediation in practice in an ESAP course : Versions of the Medical English student conference
2021
The Medical English course at the University of Oulu (Finland), which is compulsory for 200 first-year medical students, is designed to enhance professional English language communication focusing on work life relevance. The course design utilized the action-oriented approach promoted by CEFR CV (2018), to support the active use of language through various simulation activities. This paper describes specifically the final assignment of the Medical English course, which is integrated with the Clinical Psychology course. Having discussed topics in Finnish in groups, complementing the lectures in the Clinical Psychology course, students present in English what they have learnt in these discuss…
Integrated Administration of the Organizations Informational Resources
2007
Organizations grow and develop continuosly and information volume grows in the same rythm, which makes from improvement or changing the old counting systems an imperative. More and more companies, instead of continuing to invest in small applications choose integrated informational solutions, which are adapted to the user’s daily needsfrom, all decisional levels. Although apparently profitable from the costs point of view, small applications assure only the simple economical solutions between clients, partners, furnisors, and employees. For high business volume companies, this kind of applications become useless in a short time, fact that involves extra sustained investitions
Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions
2020
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function (approximation) from the corresponding energy class (which consists of the functions in $H^2$ satisfying the prescribed boundary conditions and the restrictions stipulated by the obstacle). For this purpose we use the duality method of the calculus of variations and general type error identities earlier derived for a wide class of convex variational problems. By this method, we define a combined primal--dual measure of error. It contains four terms of different natu…
C1,α-regularity for variational problems in the Heisenberg group
2017
We study the regularity of minima of scalar variational integrals of $p$-growth, $1<p<\infty$, in the Heisenberg group and prove the H\"older continuity of horizontal gradient of minima.
On the regularity of very weak solutions for linear elliptic equations in divergence form
2020
AbstractIn this paper we consider a linear elliptic equation in divergence form $$\begin{aligned} \sum _{i,j}D_j(a_{ij}(x)D_i u )=0 \quad \hbox {in } \Omega . \end{aligned}$$ ∑ i , j D j ( a ij ( x ) D i u ) = 0 in Ω . Assuming the coefficients $$a_{ij}$$ a ij in $$W^{1,n}(\Omega )$$ W 1 , n ( Ω ) with a modulus of continuity satisfying a certain Dini-type continuity condition, we prove that any very weak solution $$u\in L^{n'}_\mathrm{loc}(\Omega )$$ u ∈ L loc n ′ ( Ω ) of (0.1) is actually a weak solution in $$W^{1,2}_\mathrm{loc}(\Omega )$$ W loc 1 , 2 ( Ω ) .
Asymptotic mean value formulas for parabolic nonlinear equations
2021
In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge–Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of dynamic programming principles for certain two-player, zero-sum games. peerReviewed
On some partial data Calderón type problems with mixed boundary conditions
2021
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. T…
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.
Asymptotic Mean-Value Formulas for Solutions of General Second-Order Elliptic Equations
2022
Abstract We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and supremum, of linear operators. The families of equations that we consider include well-known operators such as Pucci, Issacs, and k-Hessian operators.