Elliptic operators and maximal regularity on periodic little-H\"older spaces

We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is satisfied in the setting of periodic little-H\"older spaces, provided the coefficients of the differential operator satisfy minimal regularity assumptions. We address parameter-dependent elliptic equations, deriving invertibility and resolvent bounds which lead to results on generation of analytic semigroups. We also demonstrate that the techniques and results of the paper hold for elliptic differential operators with operator-valued coefficients, in the setting of vector-valued functions.Comment: 27 pages, submitted for publication in Journal of Evolution Equation

The surface diffusion and the Willmore flow for uniformly regular hypersurfaces

We consider the surface diffusion and Willmore flows acting on a general class of (possibly non-compact) hypersurfaces parameterized over a uniformly regular reference manifold possessing a tubular neighborhood with uniform radius. The surface diffusion and Willmore flows each give rise to a fourth-order quasilinear parabolic equation with nonlinear terms satisfying a specific singular structure. We establish well-posedness of both flows for initial surfaces that are $C^{1+\alpha}$-regular and parameterized over a uniformly regular hypersurface. For the Willmore flow, we also show long-term existence for initial surfaces which are $C^{1+\alpha}$-close to a sphere, and we prove that these solutions become spherical as time goes to infinity.Comment: 22 page

Stability and Bifurcation of Equilibria for the Axisymmetric Averaged Mean Curvature Flow

We study the averaged mean curvature ow, also called the volume preserving mean curvature ow, in the particular setting of axisymmetric surfaces embedded in R3 satisfying periodic boundary conditions. We establish analytic well-posedness of the ow within the space of little-Holder continuous surfaces, given rough initial data. We also establish dynamic properties of equilibria, including stability, instability, and bifurcation behavior of cylinders, where the radius acts as a bifurcation parameter

An Abode for Therapy: Rediscovering the Lost Art of the Home Visit

The home visit is a service which began in early social work practice where the worker would visit the client in their home to ensure best practices. The literature and dominant beliefs of social workers highlight therapy in an individual’s home environment as an avenue of practice filled with difficulties, justifying abandonment of this method of service. This study examined the experiences of in-home therapists who provide services to individuals and families in order to explore how their experiences either aligned or contradicted the current literature. Therapists were recruited through convenience and snowball sampling. Using a focus group qualitative design, four in-home therapists discussed their experiences of conducting therapy in a client’s environment and how they were able to increase the effectiveness of therapeutic intervention through utilizing the client’s surrounding atmosphere. Participants identified increased effectiveness in the home setting regarding assessment, empowerment, rapport building, and ethical services. Participants also identified strengths in this setting regarding confidentiality and boundary setting, two areas identified as difficulties in the literature. The implications created from this study articulate the enhanced ability of assessment when conducted through a home-visit and the importance of social work education to incorporate in-home therapy as a method of practice to class curriculum

Assessment of Economic and Social Benefits of Day Care and a Budget Proposal for a Hypothetical Day Care Center

This 31 page thesis examines the history of child care, women in the workforce, and a proposal for a day care center

An Abode for Therapy: Rediscovering the Lost Art of the Home Visit

The home visit is a service which began in early social work practice where the worker would visit the client in their home to ensure best practices. The literature and dominant beliefs of social workers highlight therapy in an individual’s home environment as an avenue of practice filled with difficulties, justifying abandonment of this method of service. This study examined the experiences of in-home therapists who provide services to individuals and families in order to explore how their experiences either aligned or contradicted the current literature. Therapists were recruited through convenience and snowball sampling. Using a focus group qualitative design, four in-home therapists discussed their experiences of conducting therapy in a client’s environment and how they were able to increase the effectiveness of therapeutic intervention through utilizing the client’s surrounding atmosphere. Participants identified increased effectiveness in the home setting regarding assessment, empowerment, rapport building, and ethical services. Participants also identified strengths in this setting regarding confidentiality and boundary setting, two areas identified as difficulties in the literature. The implications created from this study articulate the enhanced ability of assessment when conducted through a home-visit and the importance of social work education to incorporate in-home therapy as a method of practice to class curriculum

Perturbed Obstacle Problems in Lipschitz Domains: Linear Stability and Non-degeneracy in Measure

We consider the classical obstacle problem on bounded, connected Lipschitz domains $D \subset \mathbb{R}^n$. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right hand side and the boundary data for obstacle problems. In particular, we show that the Lebesgue measure of the symmetric difference between two contact sets is linearly comparable to the $L^1$-norm of perturbations in the data.Comment: 9 page