Jyotshana V. Prajapat
@mu.ac.in
Professor, Department of Mathematics
University of Mumbai
Scopus Publications
Scopus Publications
Jyotshana V. Prajapat and Anoop Varghese
Springer Science and Business Media LLC
Vandana Sharma and Jyotshana V. Prajapat
American Institute of Mathematical Sciences (AIMS)
<p style='text-indent:20px;'>We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions on an evolving domain. Using a Lyapunov functional and duality arguments, we establish the existence of component wise non-negative global solutions.</p>
Avetik Arakelyan, , Henrik Shahgholian, Jyotshana V. Prajapat, , and
American Institute of Mathematical Sciences (AIMS)
In this paper we shall initiate the study of the two-and multi-phase quadrature surfaces (QS), which amounts to a two/multi-phase free boundary problems of Bernoulli type. The problem is studied mostly from a potential theoretic point of view that (for two-phase case) relates to integral representation \\begin{document}$\\int_{\\partial Ω^+} g h (x) \\ dσ_x - \\int_{\\partial Ω^-} g h (x) \\ dσ_x= \\int h dμ \\ ,$ \\end{document} where \\begin{document} $dσ_x$ \\end{document} is the surface measure, \\begin{document} $μ= μ^+ - μ^-$ \\end{document} is given measure with support in (a priori unknown domain) \\begin{document} $Ω=Ω^+\\cupΩ^-$ \\end{document} , \\begin{document} $g$ \\end{document} is a given smooth positive function, and the integral holds for all functions \\begin{document} $h$ \\end{document} , which are harmonic on \\begin{document} $\\overline Ω$ \\end{document} . Our approach is based on minimization of the corresponding two-and multi-phase functional and the use of its one-phase version as a barrier. We prove several results concerning existence, qualitative behavior, and regularity theory for solutions. A central result in our study states that three or more junction points do not appear.
Erik Lindgren and Jyotshana V. Prajapat
Springer Science and Business Media LLC
B. Emamizadeh and J. V. Prajapat
Springer Science and Business Media LLC
Behrouz Emamizadeh, Jyotshana V. Prajapat, and Henrik Shahgholian
Springer Science and Business Media LLC
Jyotshana V. Prajapat
The Mathematical Society of the Republic of China
Here we obtain a Taylor’s expansion of the function ρ(x, r) =
|B(x,r)|
|B(x,r)∩Ω|
for r small and x ∈ ∂Ω where the boundary of domain Ω is
assumed to be analytic. The coefficients are expressed as recurrence relation
and it is proved yhat the series is odd.
S. Vega, J. V. Prajapat, and A. A. Al Mazrooei
Society of Exploration Geophysicists
Fluid substitution is used to predict potential changes in seismic data due to production in oil reservoirs. The fluid changes in clastic rocks are often predicted by the Gassmann equation. However, the applicability of Gassmann's equation in carbonates is not well understood. Apparently, part of this failure is due to the violation of the assumption of a constant shear modulus for different fluids (Baechle et al., 2005; Adam et al., 2006), but it is not clear yet.
Chang-Shou Lin and Jyotshana V. Prajapat
Springer Science and Business Media LLC
Chang-Shou Lin and Jyotshana V. Prajapat
Elsevier BV
Chang-Shou Lin and Jyotshana V. Prajapat
Elsevier BV
R. Magnanini, J. Prajapat, and S. Sakaguchi
American Mathematical Society (AMS)
We establish a relationship between stationary isothermic surfaces and uniformly dense domains. A stationary isothermic surface is a level surface of temperature which does not evolve with time. A domain Ω \\Omega in the N N -dimensional Euclidean space R N \\mathbb {R}^N is said to be uniformly dense in a surface Γ ⊂ R N \\Gamma \\subset \\mathbb {R}^N of codimension 1 1 if, for every small r > 0 , r>0, the volume of the intersection of Ω \\Omega with a ball of radius r r and center x x does not depend on x x for x ∈ Γ . x\\in \\Gamma . We prove that the boundary of every uniformly dense domain which is bounded (or whose complement is bounded) must be a sphere. We then examine a uniformly dense domain with unbounded boundary ∂ Ω \\partial \\Omega , and we show that the principal curvatures of ∂ Ω \\partial \\Omega satisfy certain identities. The case in which the surface Γ \\Gamma coincides with ∂ Ω \\partial \\Omega is particularly interesting. In fact, we show that, if the boundary of a uniformly dense domain is connected, then (i) if N = 2 N=2 , it must be either a circle or a straight line and (ii) if N = 3 , N=3, it must be either a sphere, a spherical cylinder or a minimal surface. We conclude with a discussion on uniformly dense domains whose boundary is a minimal surface.
J. Prajapat and Mythily Ramaswamy
Walter de Gruyter GmbH
Abstract Here we study the precise blow-up behaviour and obtain a priori estimates for the finite energy C2-solutions of the equation on the odd dimensional spheres S2n+1 with standard CR structure, as the exponent for p ∈ , Q = 2n + 2 is the homogeneous dimension.
I. Birindelli and J. Prajapat
Mathematical Sciences Publishers
In this paper we prove some monotonicity results for solutions of semilinear equations in nilpotent, stratified groups. We also prove a partial symmetry result for solutions of nonlinear equations on the Heisenberg group.
J. Prajapat and G. Tarantello
Cambridge University Press (CUP)
In the plane R2, we classify all solutions for an elliptic problem of Liouville type involving a (radial) weight function. As a consequence, we clarify the origin of the non-radially symmetric solutions for the given problem, as established by Chanillo and Kiessling.For a more general class of Liouville-type problems, we show that, rather than radial symmetry, the solutions always inherit the invariance of the problem under inversion with respect to suitable circles. This symmetry result is derived with the help of a 'shrinking-sphere' method.
F. Brock and J. Prajapat
Springer Science and Business Media LLC
I. Birindelli and J. Prajapat
Informa UK Limited
Jyotshana Prajapat
Duke University Press
S. Kumaresan and Jyotshana Prajapat
Duke University Press